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Question Number 65915 by mathmax by abdo last updated on 05/Aug/19
$${let}\:{p}\:{prime}\:{not}\:\mathrm{0}\:\:{and}\:{n}\:{integr}\:/\mathrm{1}\leqslant{n}<{p}\:{prove}\:{that} \\ $$ $$\frac{\left({p}−\mathrm{1}\right)\left({p}−\mathrm{2}\right)....\left({p}−{n}\right)}{{n}!}\:−\left(−\mathrm{1}\right)^{{n}} \:\:{is}\:{integr}\:{and}\:{divided}\:{by}\:{p} \\ $$