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Questions where prime numbers play a key-role, such as: questions on the distribution of prime numbers (twin primes, gaps between primes, Hardy–Littlewood conjectures, etc); questions on prime numbers with special properties (Wieferich prime, Wolstenholme prime, etc.). This tag is often used as a specialized tag in combination with the top-level tag nt.number-theory and (if applicable) analytic-number-theory.

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what are all possible pairs (k,m) such that n=2k^2+ m^2

I am working on a problem in number theory and would like to count all possible ways to partition an integer $n\geq 1$ into pairs $(k,m)$ of positive integers such that $n=2k^2+m^2$ and $n=4k^2+m^2$. …
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