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Ali
Ali
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I am working on a problem in number theory and would like to count all possible ways to partition an integer $n$$n\geq 1$ into pairs $(k,m)$ of positive integers such that $n=2k^2+m^2$ and $n=4k^2+m^2$. Let's say $s(n)$ counts all pairs $(k,m)$ such that $n=2k^2+m^2$, while $t(n)$ counts all pairs $(k,m)$ such that $n=4k^2+m^2$. what are the generating functions of $s(n), t(n)$?

I am working on a problem in number theory and would like to count all possible ways to partition an integer $n$ into pairs $(k,m)$ such that $n=2k^2+m^2$ and $n=4k^2+m^2$. Let's say $s(n)$ counts all pairs $(k,m)$ such that $n=2k^2+m^2$, while $t(n)$ counts all pairs $(k,m)$ such that $n=4k^2+m^2$. what are the generating functions of $s(n), t(n)$?

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 $n=4k^2+m^2$. Let's say $s(n)$ counts all pairs $(k,m)$ such that $n=2k^2+m^2$, while $t(n)$ counts all pairs $(k,m)$ such that $n=4k^2+m^2$. what are the generating functions of $s(n), t(n)$?

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Ali
Ali
  • 11
  • 1

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 $n$ into pairs $(k,m)$ such that $n=2k^2+m^2$ and $n=4k^2+m^2$. Let's say $s(n)$ counts all pairs $(k,m)$ such that $n=2k^2+m^2$, while $t(n)$ counts all pairs $(k,m)$ such that $n=4k^2+m^2$. what are the generating functions of $s(n), t(n)$?