<s>[INST] Sum of squares and $5\cdot2^n$ Does anyone know of a proof of the result that $5\cdot2^n$ where $n$ is a nonnegative integer is always the sum of two squares?
That is, nonzero integers $x,y$ must always exist where: 
$x^2+y^2=5\cdot2^n$
when $n$ is $0$ or a positive integer?
For example: 
$$1^2+2^2=5\cdot 2^0$$
$$1^2+3^2=5\cdot 2^1$$
$$2^2+4^2=5\cdot 2^2$$
$$2^2+6^2=5\cdot 2^3$$
 [/INST] Hint:-
$5\cdot2^n=x^2+y^2 \implies 5\cdot 2^{n+2}=(2x)^2+(2y)^2$
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