Question
1. If a, b are two distinct prime numbers then the greatest common factor of a and b is:
2. A floor function maps a real number to:
3. [2.4] + [2.9] is equal to:
4. If x, and y are positive numbers both are less than one, then the maximum value of [x + y] is equal to:
5. If [x] = [x], then:
6. [3/4] is equal to:
7. [-3/4] is equal to:
8. [[-3/4]-[-3/4]] is equal to:
9. Find x, given 7 ≡ x mod 3
10. Find x, given 27 ≡ x mod 5
11. Find x, given x ≡ 3 mod 5
12. Find x, given x ≡ 1 mod 3
13. Find x, given 183 ≡ mod x
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1. If a, b are two distinct prime numbers then the greatest common factor of a and b is: 1
2. A floor function maps a real number
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      • Illuminate\Cache\Events\CacheHit (166μs)
      • Illuminate\Cache\Events\CacheHit (117μs)
      • Illuminate\Cache\Events\CacheHit (139μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (136μs)
      • Illuminate\Cache\Events\CacheHit (108μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (106μs)
      • Illuminate\Cache\Events\CacheHit (120μs)
      • Illuminate\Cache\Events\CacheHit (104μs)
      • Illuminate\Cache\Events\CacheHit (126μs)
      • Illuminate\Cache\Events\CacheHit (112μs)
      • creating: site.layouts.app (361μs)
      • composing: site.layouts.app (17μs)
      • creating: components.canonical (292μs)
      • composing: components.canonical (69μs)
      • creating: components.open-graph (143μs)
      • composing: components.open-graph (49μs)
      • creating: site.headers.header (223μs)
      • composing: site.headers.header (53μs)
      • Illuminate\Cache\Events\CacheHit (2.06ms)
      • creating: components.footer (78μs)
      • composing: components.footer (74μs)
      • Illuminate\Cache\Events\CacheHit (622μs)
      • Illuminate\Cache\Events\CacheMissed (185μs)
      • Illuminate\Database\Events\StatementPrepared (683μs)
      • Illuminate\Database\Events\QueryExecuted (856μs)
      • eloquent.retrieved: App\Models\SubjectCat (85μs)
      • Illuminate\Cache\Events\KeyWritten (1.26ms)
      • Illuminate\Cache\Events\CacheHit (316μs)
      • Illuminate\Cache\Events\CacheHit (174μs)
      • Illuminate\Cache\Events\CacheHit (143μs)
      • Illuminate\Cache\Events\CacheHit (125μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • Illuminate\Cache\Events\CacheHit (254μs)
      • Illuminate\Cache\Events\CacheHit (376μs)
      • Illuminate\Cache\Events\CacheHit (149μs)
      • Illuminate\Cache\Events\CacheHit (132μs)
      • Illuminate\Cache\Events\CacheHit (140μs)
      • Illuminate\Cache\Events\CacheHit (131μs)
      • Illuminate\Cache\Events\CacheHit (123μs)
      • creating: components.forms.contact-us (197μs)
      • composing: components.forms.contact-us (415μs)
      • creating: components.forms.get-started (139μs)
      • composing: components.forms.get-started (117μs)
      • creating: components.forms.free-tool-download (93μs)
      • composing: components.forms.free-tool-download (131μs)
      • creating: components.forms.claim-free-worksheet (190μs)
      • composing: components.forms.claim-free-worksheet (49μs)
      • creating: components.forms.tutor-subscription-waitlist (73μs)
      • composing: components.forms.tutor-subscription-waitlist (42μs)
      • creating: components.forms.tutor-subscription-join (155μs)
      • composing: components.forms.tutor-subscription-join (49μs)
      • creating: components.forms.tutor-support (83μs)
      • composing: components.forms.tutor-support (42μs)
      • 311 x Illuminate\Cache\Events\CacheHit (17.56%)
        75.52ms
        20 x Illuminate\Database\Events\QueryExecuted (7.38%)
        31.75ms
        20 x Illuminate\Database\Events\StatementPrepared (6.62%)
        28.46ms
        11 x Illuminate\Cache\Events\CacheMissed (1.86%)
        7.99ms
        11 x Illuminate\Cache\Events\KeyWritten (1.65%)
        7.10ms
        1 x Illuminate\Foundation\Events\LocaleUpdated (1.12%)
        4.83ms
        1 x Illuminate\Routing\Events\Routing (0.32%)
        1.40ms
        1 x Illuminate\Database\Events\ConnectionEstablished (0.28%)
        1.19ms
        12 x eloquent.retrieved: App\Models\SubjectCat (0.24%)
        1.03ms
        1 x Illuminate\Routing\Events\RouteMatched (0.12%)
        533μs
        1 x composing: components.forms.contact-us (0.1%)
        415μs
        1 x creating: site.layouts.app (0.08%)
        361μs
        7 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibrary (0.07%)
        313μs
        1 x eloquent.booting: App\Models\SubjectCat (0.07%)
        296μs
        1 x creating: components.canonical (0.07%)
        292μs
        2 x eloquent.retrieved: App\Models\Subject (0.06%)
        239μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        233μs
        1 x creating: site.headers.header (0.05%)
        223μs
        1 x creating: components.breadcrumbs (0.05%)
        219μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibrary (0.05%)
        213μs
        1 x creating: components.forms.contact-us (0.05%)
        197μs
        1 x creating: homework.show (0.04%)
        192μs
        1 x creating: components.forms.claim-free-worksheet (0.04%)
        190μs
        2 x eloquent.retrieved: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.04%)
        161μs
        1 x creating: components.forms.tutor-subscription-join (0.04%)
        155μs
        1 x creating: components.open-graph (0.03%)
        143μs
        1 x creating: components.forms.get-started (0.03%)
        139μs
        1 x composing: components.forms.free-tool-download (0.03%)
        131μs
        1 x composing: components.forms.get-started (0.03%)
        117μs
        1 x eloquent.booting: App\Models\Subject (0.02%)
        106μs
        1 x creating: components.forms.free-tool-download (0.02%)
        93μs
        1 x composing: components.breadcrumbs (0.02%)
        88μs
        1 x composing: homework.show (0.02%)
        87μs
        1 x eloquent.booting: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.02%)
        84μs
        1 x creating: components.forms.tutor-support (0.02%)
        83μs
        1 x creating: components.footer (0.02%)
        78μs
        1 x composing: components.footer (0.02%)
        74μs
        1 x creating: components.forms.tutor-subscription-waitlist (0.02%)
        73μs
        1 x composing: components.canonical (0.02%)
        69μs
        1 x composing: site.headers.header (0.01%)
        53μs
        1 x composing: components.open-graph (0.01%)
        49μs
        1 x composing: components.forms.claim-free-worksheet (0.01%)
        49μs
        1 x composing: components.forms.tutor-subscription-join (0.01%)
        49μs
        1 x eloquent.booted: App\Models\HomeworkLibrary\HomeworkLibraryFile (0.01%)
        46μs
        1 x eloquent.booted: App\Models\Subject (0.01%)
        44μs
        1 x eloquent.booted: App\Models\SubjectCat (0.01%)
        43μs
        1 x composing: components.forms.tutor-subscription-waitlist (0.01%)
        42μs
        1 x composing: components.forms.tutor-support (0.01%)
        42μs
        1 x composing: site.layouts.app (0%)
        17μs
      14 templates were rendered
      • 1x homework.showshow.blade.phpblade
      • 1x components.breadcrumbsbreadcrumbs.blade.phpblade
      • 1x site.layouts.appapp.blade.phpblade
      • 1x components.canonicalcanonical.blade.phpblade
      • 1x components.open-graphopen-graph.blade.phpblade
      • 1x site.headers.headerheader.blade.phpblade
      • 1x components.footerfooter.blade.phpblade
      • 1x components.forms.contact-uscontact-us.blade.phpblade
      • 1x components.forms.get-startedget-started.blade.phpblade
      • 1x components.forms.free-tool-downloadfree-tool-download.blade.phpblade
      • 1x components.forms.claim-free-worksheetclaim-free-worksheet.blade.phpblade
      • 1x components.forms.tutor-subscription-waitlisttutor-subscription-waitlist.blade.phpblade
      • 1x components.forms.tutor-subscription-jointutor-subscription-join.blade.phpblade
      • 1x components.forms.tutor-supporttutor-support.blade.phpblade
      uri
      GET college-homework-library/{category}/{subject}/{id}
      middleware
      web, utm.parameters
      controller
      App\Http\Controllers\HomeworkLibraryController@show
      namespace
      where
      as
      homework.show
      file
      app/Http/Controllers/HomeworkLibraryController.php:79-176
      20 statements were executed, 5 of which were duplicates, 15 unique. Show only duplicated45.31ms
      • Connection Establishedtwenty4_siteHomeworkLibraryController.php#91
        Backtrace
        • 13. app/Http/Controllers/HomeworkLibraryController.php:91
        • 14. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 15. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 16. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary` where `status` = 'published' and `price` > 0 and `solutionslibrary`.`id` = '57286' limit 1
        11.39mstwenty4_siteHomeworkLibraryController.php#97
        Bindings
        • 0: published
        • 1: 0
        • 2: 57286
        Backtrace
        • 16. app/Http/Controllers/HomeworkLibraryController.php:97
        • 17. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 19. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 20. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subjects` where `subjects`.`id` in (15)
        980μstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` in (57286)
        3mstwenty4_siteHomeworkLibraryController.php#97
        Backtrace
        • 21. app/Http/Controllers/HomeworkLibraryController.php:97
        • 22. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 23. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 24. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
        • 25. vendor/laravel/framework/src/Illuminate/Routing/Route.php:205
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.42mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 3
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 26. app/Http/Controllers/HomeworkLibraryController.php:105
        • 27. vendor/laravel/framework/src/Illuminate/Routing/Controller.php:54
        • 28. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
        • 29. vendor/laravel/framework/src/Illuminate/Routing/Route.php:260
      • select * from `solutionslibrary` where `id` <> 57286 and `subject` = 15 and `status` = 'published' and `price` > 0 order by RAND() limit 6
        10.54mstwenty4_siteHomeworkLibraryRepository.php#30
        Bindings
        • 0: 57286
        • 1: 15
        • 2: published
        • 3: 0
        Backtrace
        • 14. app/Repositories/HomeworkLibraryRepository.php:30
        • 15. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 16. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 18. app/Repositories/HomeworkLibraryRepository.php:39
        • 19. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `subjects` where `subjects`.`id` in (15)
        950μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 21. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 23. app/Repositories/HomeworkLibraryRepository.php:39
        • 24. app/Http/Controllers/HomeworkLibraryController.php:139
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 57286 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'question' order by `order` asc, `id` asc
        1.26mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 57286
        • 1: question
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:58
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 57286 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'teaser' order by `order` asc, `id` asc
        990μstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 57286
        • 1: teaser
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:69
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `solutionslibrary_files` where `solutionslibrary_files`.`solutionlib_id` = 57286 and `solutionslibrary_files`.`solutionlib_id` is not null and `publish` = 'solution' order by `order` asc, `id` asc
        2.55mstwenty4_siteHomeworkLibrary.php#260
        Bindings
        • 0: 57286
        • 1: solution
        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
        • 16. app/Transformers/HomeworkLibrary/HomeworkLibraryTransformer.php:80
        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
        • 20. vendor/league/fractal/src/TransformerAbstract.php:107
        • 21. vendor/league/fractal/src/Scope.php:383
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        1.03mstwenty4_siteHomeworkLibrary.php#201
        Bindings
        • 0: 3
        Backtrace
        • 20. app/Models/HomeworkLibrary/HomeworkLibrary.php:201
        • 32. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
        • 33. vendor/laravel/framework/src/Illuminate/View/Engines/PhpEngine.php:58
        • 34. vendor/livewire/livewire/src/ComponentConcerns/RendersLivewireComponents.php:69
        • 35. vendor/laravel/framework/src/Illuminate/View/Engines/CompilerEngine.php:70
      • select * from `subject_cats` where `subject_cats`.`id` = 1 limit 1
        1.06mstwenty4_siteSubject.php#100
        Bindings
        • 0: 1
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 3 limit 1
        980μstwenty4_siteSubject.php#100
        Bindings
        • 0: 3
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 4 limit 1
        1.33mstwenty4_siteSubject.php#100
        Bindings
        • 0: 4
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 10 limit 1
        1.13mstwenty4_siteSubject.php#100
        Bindings
        • 0: 10
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 33 limit 1
        1.05mstwenty4_siteSubject.php#100
        Bindings
        • 0: 33
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 11 limit 1
        1.03mstwenty4_siteSubject.php#100
        Bindings
        • 0: 11
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 5 limit 1
        1.2mstwenty4_siteSubject.php#100
        Bindings
        • 0: 5
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 34 limit 1
        1.27mstwenty4_siteSubject.php#100
        Bindings
        • 0: 34
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 31 limit 1
        1.14mstwenty4_siteSubject.php#100
        Bindings
        • 0: 31
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 34. vendor/laravel/framework/src/Illuminate/Filesystem/Filesystem.php:110
      • select * from `subject_cats` where `subject_cats`.`id` = 36 limit 1
        1.01mstwenty4_siteSubject.php#100
        Bindings
        • 0: 36
        Backtrace
        • 18. app/Models/Subject.php:100
        • 19. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
        • 20. vendor/laravel/framework/src/Illuminate/Cache/CacheManager.php:419
        • 22. app/Models/Subject.php:101
        • 28. view::components.footer:170
      App\Models\SubjectCat
      12SubjectCat.php
      App\Models\HomeworkLibrary\HomeworkLibrary
      7HomeworkLibrary.php
      App\Models\Subject
      2Subject.php
      App\Models\HomeworkLibrary\HomeworkLibraryFile
      2HomeworkLibraryFile.php
          _token
          rwJ4gmvXrkEQhZQqA65KclMs3ZNjjKAC5tPfpY3V
          utm_source
          direct
          redirectUrl
          /college-homework-library/Computer-Science/Discrete-Math/57286
          _previous
          array:1 [ "url" => "https://staging.dev.24houranswers.com/college-homework-library/Computer-Scienc...
          _flash
          array:2 [ "old" => [] "new" => [] ]
          PHPDEBUGBAR_STACK_DATA
          []
          path_info
          /college-homework-library/Computer-Science/Discrete-Math/57286
          status_code
          200
          
          status_text
          OK
          format
          html
          content_type
          text/html; charset=UTF-8
          request_query
          []
          
          request_request
          []
          
          request_headers
          0 of 0
          array:21 [ "priority" => array:1 [ 0 => "u=0, i" ] "accept-encoding" => array:1 [ 0 => "gzip, deflate, br, zstd" ] "sec-fetch-dest" => array:1 [ 0 => "document" ] "sec-fetch-user" => array:1 [ 0 => "?1" ] "sec-fetch-mode" => array:1 [ 0 => "navigate" ] "sec-fetch-site" => array:1 [ 0 => "none" ] "accept" => array:1 [ 0 => "text/html,application/xhtml+xml,application/xml;q=0.9,image/avif,image/webp,image/apng,*/*;q=0.8,application/signed-exchange;v=b3;q=0.7" ] "user-agent" => array:1 [ 0 => "Mozilla/5.0 AppleWebKit/537.36 (KHTML, like Gecko; compatible; ClaudeBot/1.0; +claudebot@anthropic.com)" ] "upgrade-insecure-requests" => array:1 [ 0 => "1" ] "sec-ch-ua-platform" => array:1 [ 0 => ""Windows"" ] "sec-ch-ua-mobile" => array:1 [ 0 => "?0" ] "sec-ch-ua" => array:1 [ 0 => ""HeadlessChrome";v="129", "Not=A?Brand";v="8", "Chromium";v="129"" ] "cache-control" => array:1 [ 0 => "no-cache" ] "pragma" => array:1 [ 0 => "no-cache" ] "x-amzn-trace-id" => array:1 [ 0 => "Root=1-680a83cb-715b862404bff1ea35e505b5" ] "host" => array:1 [ 0 => "staging.dev.24houranswers.com" ] "x-forwarded-port" => array:1 [ 0 => "443" ] "x-forwarded-proto" => array:1 [ 0 => "https" ] "x-forwarded-for" => array:1 [ 0 => "3.143.170.30" ] "content-length" => array:1 [ 0 => "" ] "content-type" => array:1 [ 0 => "" ] ]
          request_cookies
          []
          
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