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If the factorization of the integer $n$ is either $n=p_1^{a_1}\cdots p_s^{a_s}$ or $n=2p_1^{a_1}\cdots p_s^{a_s}$, where all $p_i$ are primes of form $4k+1$, then $n$ has $2^{s-1}$ representations as $n=a^2+b^s$, where $\gcd(a,b)=1$ (see for example this post ). The SAGE command sum_of_k_squares(2,n) will give one such representation. Is there a way to find all of them?

If the factorization of the integer $n$ is either $n=p_1^{a_1}\cdots p_s^{a_s}$ or $n=2p_1^{a_1}\cdots p_s^{a_s}$, where all $p_i$ are primes of form $4k+1$, then $n$ has $2^{s-1}$ representations as $n=a^2+b^s$, $n=a^2+b^2$, where $\gcd(a,b)=1$ (see for example this post ). The SAGE command sum_of_k_squares(2,n) will give one such representation. Is there a way to find all of them?