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Lagrange's four square theorem states that each $m\in\mathbb N=\{0,1,2,\ldots\}$ can be written as a sum of four squares. Recently, I found that the diophantine equation $x^2+7y^2=2^n$ has certain ...

It's known that the number of representations of an integer $k$ by sum of two squares is $$ 4\;\sum_{d|k}\left(\frac{-4}{d}\right) $$ or $$ 4\sum_{d|k,\; d \textrm{ odd}} (-1)^{\frac{d-1}{2}}= 4(d_1(k)...