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Let a, b and n 2 be integers. (a) Prove that if a b (mod n), then ak bk (mod nk) for
Chapter 7, Problem 12(choose chapter or problem)
QUESTION:
Let a, b and n 2 be integers. (a) Prove that if a b (mod n), then ak bk (mod nk) for every positive integer k. (b) Disprove: If ak bk (mod n) for some integer k, then a b (mod n).
Questions & Answers
QUESTION:
Let a, b and n 2 be integers. (a) Prove that if a b (mod n), then ak bk (mod nk) for every positive integer k. (b) Disprove: If ak bk (mod n) for some integer k, then a b (mod n).
ANSWER:Step 1 of 3
The integer a is congruent to integer b modulo integer n is written in mathematical notation as