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If $n = x^5 - y^5 - z^5$, where $x$, $y$, and $z$ are positive integers, which of the following could not be a value for $n$?

Challenge: Solve without …

Find all pairs $(x, y)$ of positive integers such that they satisfy the following equation.

$e^{t^2-ty^7}e^{te^{t-y^7}}=\left(\frac{x^7e^{x^7}+y^7e^{x^7}}{t}\right)^t e^{x^7e^{x^7}+y^7e^{x^7}}$

Here, $t=\num{21870000000}.$

Submit your answer as the sum of sums of all such …

Find the number of tetrahedrons in which three of its face triangles have right angles all at the same vertex, and all four of its face triangles have integer areas …

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