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let-p-prime-not-0-and-n-integr-1-n-lt-p-prove-that-p-1-p-2-p-n-n-1-n-is-integr-and-divided-by-p-

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

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