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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
3 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 $$\text{mod n}$$ · 2 weeks, 3 days ago

Thank you so much · 2 weeks, 2 days ago

I mean $$\text{mod (n-1)}$$ · 2 weeks, 3 days ago