Hi, I'm doing a physics calculation, and along the way, I've run up against a curious math problem. I'm sure this is a rather classic problem in mathematics, but I'm just not acquainted with the subject enough to answer it, or even look it up, so hopefully someone can point me in the right direction.(adsbygoogle = window.adsbygoogle || []).push({});

For a given positive integer [itex]\ell>0[/itex] and another positive integer [itex]m\leq\ell[/itex], for what values of a list of (zero or positive) integers [itex]\{k_1\geq0,\,k_2\geq0,\,\ldots,\,k_\ell\geq0\}[/itex] satisfies the following simultaneous pair of equations?

[tex]\sum_{n=1}^\ell k_n = m[/tex]

[tex]\sum_{n=1}^\ell n k_n = \ell[/tex]

Even the name given to the problem would point me in the right direction. Thanks!!!

Also, please do not treat me like a student :-)

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# Sum over integers

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