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An arithmetic theorem. (Théorème d’arithmétique.) (French) JFM 13.0136.03
Ist \[ N=\alpha + \beta+\cdots+pq+p_{1}q_{1}+ \cdots + rst, \] so ist \(N\)! teilbar durch das Product \[ \alpha! \beta! \dots{}(p!)^{q}q!(p_{1}!)^{q_{1}}q_{1}!\dots{}(r)^{st}(s!)^{t}t! \]

MSC:
11A99 Elementary number theory
11B65 Binomial coefficients; factorials; \(q\)-identities
Keywords:
divisibility
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