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Integrality of a quotient of Fermat numbers

The fraction equals $$\prod_{k=0}^{n-1}\frac{2^{2^m-2^k}-1}{2^{2^n-2^k}-1},$$ hence it suffices to show that $$\prod_{k=0}^{n-1}\frac{x^{2^m-2^k}-1}{x^{2^n-2^k}-1}\in\mathbb{Z}[x].$$ The numerator and ...
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Which theorems have Pythagoras' Theorem as a special case?

Dijkstra's generalization of the Pythagorean theorem Let a triangle have sides $a,b,c>0$ with corresponding opposite angles $\alpha,\beta,\gamma$. Then $\alpha+\beta=\gamma\equiv a^2+b^2=c^2$ $\...

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