Quote:
Originally Posted by Yak
A counterexample may be sufficient, but since you were working with modular arithmetic:
n^3 + 2n ~ 0mod2 (divisible by 2, no remainder, ~ means congruent)
n^3 + 2n = 2k
n^3 + 2n - 2k = 0
let k = n
n^3 + 2n - 2n = 0
n^3 = 0
Since n^3 cannot = 0 when n >=2, it's disproven.
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I do not understand the transition from step 1 to 2 but I do not doubt it.
Once that is accomplished the rest of your proof is simple, clear and well done.
My career has not involved mod/etc except tangentially but for some reason I'v always enjoyed geometric proofs.