Let n E N. Suppose that n > 1, and that (n − 1)! = −1 (mod n). Prove that n is a prime number. The converse to this result, known as Wilson's Theorem, is also true, but has a slightly lengthier proof; see [AR89, Section 3.5] or [Ros05, Section 6.1] for details.

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Q: 1. Prove that 35121 (mod 1024).

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Q: 13. a. Prove that for every integer n 1, 10" = (-1)" (mod 11). |

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Q: Proposition 6.1.21. A number is divisible by 11 if and only if the alternat- ing sums of the digits…

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Q: 7. Let n E Z. Prove that 9n3 6 (mod 27).

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Q: 20.What is the value of n such that (24  is congruent to 58 mod n) ? a.13 b.17 c.-34 d.-13

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