Question
P1. Convert (7206)8 and (AOEB)16 to binary.

P2. Express gcd(84, 119) as a linear combination of 84 and 119.

P3. Use the Chinese Remainder Theorem to solve the following system of linear congruences: x ≡ 1 mod 4 x ≡ 2 mod 5 x ≡ 3 mod 7

P4. Encrypt the message GRIZZLY BEARS using blocks of five letters and the transposition cipher based on the permutation of {1,2,3,4,5} with σ(1) = 3, σ(2)=5, σ(3)=1, σ(4) = 2 and σ(5)=4. For this problem, use the letter X as many times as necessary to fill out the final block of fewer than 5 letters.

P5. A check digit a13 for an ISBN-13 with initial digits a1, a2, …, a12 is determined by the congruence {(a1 + a3 +….+ a13) + 3(a2 + a4 + … +a12)} ≡ 0 mod 10. Determine if each of the following 13‐digit numbers is a valid ISBN‐13. a. 978‐0‐073‐20679-1 b. 978‐0-201‐10179‐9

P6. Determine the plaintext for the RSA ciphertext 2169 0628 5540 2169 6560 6401 4829 with n = 7747 (p = 61 and q = 127) and e=17.
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P1. Convert (7206)8 and (AOEB)16 to binary.
Answer:
We first convert the number from octal to decimal and then to binary.
(7206)8=7*8^3+2*8^2+0*8+6=7*512+2*64+6=3,584+134=3,718
Now we transform the decimal number into binary.
3,718:2=1,859 remainder 0
1,859:2= 929 remainder 1
929:2=464 remainder 1
464:2=232 remainder 0
232:2=116 remainder 0
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        • 18. vendor/laravel/framework/src/Illuminate/Routing/ControllerDispatcher.php:43
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        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
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        7.24mstwenty4_siteHomeworkLibraryController.php#97
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        • 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
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      • select * from `subjects` where `subjects`.`id` in (15)
        990μstwenty4_siteHomeworkLibraryRepository.php#30
        Backtrace
        • 19. app/Repositories/HomeworkLibraryRepository.php:30
        • 20. vendor/laravel/framework/src/Illuminate/Cache/Repository.php:397
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        1.35mstwenty4_siteHomeworkLibrary.php#260
        Bindings
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        Backtrace
        • 15. app/Models/HomeworkLibrary/HomeworkLibrary.php:260
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        • 19. vendor/league/fractal/src/TransformerAbstract.php:128
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