Question 1042957
No. N (double stroke N, i.e. \mathbb{N} *[tex \large \mathbb{N}]) is the set of natural numbers, which are non-negative (some restrict to positive integers), so a valid counterexample would be a set of natural number values for a, b, and n with *[tex \large n \ge 2], such that the statement does not hold.


A valid counterexample: a = 2, b = 4, c = 8. It's true that *[tex \large 2^3 \equiv 4^3 \pmod{8}] but *[tex \large 2 \not\equiv 4 \pmod{8}].