Math

Prove that a^3 ≡ a (mod 3) for every positive integer a.

What I did:

Assume a^3 ≡ a (mod 3) is true for every positive integer a.
Then 3a^3 ≡ 3a (mod 3).
(3a^3 - 3a)/3 = k, where k is an integer
a^3 - a = k
Therefore, a^3 ≡ a (mod 3).

Is this a valid method for proving?

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  1. not really. Try this:

    math.stackexchange.com/questions/992245/prove-that-if-a-in-mathbbz-then-a3-equiv-amod-3

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