Prove either by contradiction or contraposition (using Fundamental Theorem of Arithmetic in either case) that:
$$ ∀k ∈ \mathbb{Z}, [3|(k-2) → 3 |(k^2 - 1)] $$
Any help would be great! Thanks!
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$$k^2-1=(k-2)(k+2)+3$$ – lab bhattacharjee Aug 27 '14 at 04:57
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A similar question, without the FTA request, was asked and answered yesterday. The FTA part is rather unnatural, one needs much less. – André Nicolas Aug 27 '14 at 05:05
