3.11. (a) Let n be any integer such that n is congruent to 0 (mod 7)....

3.11. (a) Let n be any integer such that n is congruent to 0 (mod 7). For any positive integer k, what is the remainder when n^k is divided by 7?

(b) Let n be any integer such that n is congruent to 1 (mod 7). For any positive integer k, what is the remainder when n^k is divided by 7?

(c) Let n be any integer such that n is congruent to 2 (mod 7). For any nonnegative integer k, what is the remainder when (i) n^3k is divided by 7? (ii) n^3k+1 is divided by 7? (iii) when n^3k+2 is divided by 7?

(d) Let n be any integer such that n is congruent to 3 (mod 7). For any nonnegative integer k, what is the remainder when (i) n^3k is divided by 7? (ii) n^3k+1 is divided by 7? (iii) when n^3k+2 is divided by 7?

Expert Solution

Colby Messinger answered 1 year ago

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