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Question Number 14109 by FilupS last updated on 28/May/17
(a^p −a) mod p = 0 when is this true? a,p∈Z
$$\left({a}^{{p}} −{a}\right)\:\mathrm{mod}\:{p}\:=\:\mathrm{0} \\ $$$$\mathrm{when}\:\mathrm{is}\:\mathrm{this}\:\mathrm{true}? \\ $$$${a},{p}\in\mathbb{Z} \\ $$
Commented by ajfour last updated on 28/May/17
a=p or just a=1.
$${a}={p}\:\:\:\:\:{or}\:{just} \\ $$$${a}=\mathrm{1}. \\ $$
Commented by nume1114 last updated on 28/May/17
or p is prime. (fermat′s little theorem)
$${or}\:{p}\:{is}\:{prime}. \\ $$$$\left({fermat}'{s}\:{little}\:{theorem}\right) \\ $$
Commented by RasheedSindhi last updated on 28/May/17
If p is prime and (a,p)=1.
$$\mathrm{If}\:\mathrm{p}\:\mathrm{is}\:\mathrm{prime}\:\mathrm{and}\:\left(\mathrm{a},\mathrm{p}\right)=\mathrm{1}. \\ $$

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