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Number Theory Proof

Let \(n\geqslant 2\) and \(k\) be any positive integers. Prove that \((n-1)^2 | (n^k - 1) \) if and only if \((n-1) | k \).

Note by أحمد الحلاق
7 months, 4 weeks ago

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Just use the identity

\(\frac{n^k-1}{n-1}=n^{k-1}+\ldots+n^1+1\)

and take the resulting equation \(\text{mod n}\) Wen Z · 7 months, 3 weeks ago

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@Wen Z Thank you so much Sattik Biswas · 7 months, 3 weeks ago

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@Wen Z I mean \(\text{mod (n-1)}\) Wen Z · 7 months, 3 weeks ago

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Could you please provide a solution? Sattik Biswas · 7 months, 3 weeks ago

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