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Given $\left(x + \sqrt{1+y^2}\right)\left(y + \sqrt{1+x^2}\right) = 1$, prove $\left(x + \sqrt{1+x^2}\right)\left(y + \sqrt{1+y^2}\right) = 1$.

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All integers from 1 to 73 are recorded in a sequence such that each number

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If $-1\leq x, y \leq 1$ and $x\sqrt{1-y^2} + y\sqrt{1-x^2} = 1$, find $x^2+y^2$

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Sum of Digits of 4th Powers

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A question about a possible solution to A5 from Putnam 2018

Spies - how to get an inequality?

A question from 1989 leningrad mathematical olympiad

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$\dfrac{\cos \alpha}{\cos (\beta-\gamma)}$

If $|MA|^2=|MB|^2+|MC|^2$. Find the $\angle BMC=?$

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Given $\left(x + \sqrt{1+y^2}\right)\left(y + \sqrt{1+x^2}\right) = 1$, prove $\left(x + \sqrt{1+x^2}\right)\left(y + \sqrt{1+y^2}\right) = 1$.

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