Select the following statements that are true. a 0 for any integer a > 0 31000 = 1 (mod 10) 2022 1 (mod 3) n(n + 1) = 0 (mod 2) for any integer n 3n+ 1 = 0 (mod 2) for any integer n 7 999 37 | 999 365 1 (mod 7)

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Q: Let x be an integer coprime to 1450 that is not congruent to 1 modulo 1450. Suppose we know that x1…

Q: 4. For any integer n, show that if n³ = 1 (mod 47), then n = 1 (mod 47).

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Q: Compute or show that it does not exist. (a) 149-¹ (mod 200); (b) 95-¹ (mod 323).

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Q: Show that for every integer n, either 3 | n or n² = 1 (mod 3).

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Q: Find 134! (mod 713). Your answer should be an integer of the form all your steps.

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Q: Problem 7 Suppose b is any integer. Ifb mod 12 = 5, what is 6b mod 12? In other words, if division…

Q: Select the following statements that are true. 261000 = 1 (mod 3) (2022) 10 (FC6) 16 In Z6, 2¹⁰ = 2…

Q: Is 7|(15+20): True or False? 28 is congruent to 42 modulo 6: True or False?

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Q: (d) For all integers a and b, if ab = 7 (mod 12), then either a = 1 (mod 12) or a = 7 (mod 12).

Q: (32³ mod 13)² mod 11

Q: 1)For each of the following statements write a short proof. Be sure to state the method of proof you…

Q: The multiplicative inverse of 103 (mod 120) * O is 7(mod 120) O None of these is 50(mod 120) is…

Q: Evaluate the expressions. (a) 50 div 7 7.143 (b) 50 mod 7 1 ]x