let $p, q$ be prime number such that $p >q$ and $f$ be integer polynomial such that :$f:\mathbb{N\times N}\to \mathbb{N}$ , I invesitagted in the web to find such integer polynomial for which: $f(p,q)$ for which $(p-q)!=p!-q!+f(p,q)$ but I didn't got , I have used properties of gamma function by means functional function satisfied by Gamma but I can't up to the disered function $f(p,q)$, Any help ?
2026-03-30 06:15:52.1774851352
Is there known integer polynomial $f(p,q)$ for which $(p-q)!=p!-q!+f(p,q)$?
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