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Always mod 1?!

Prove or disprove: \[ a^{p-1} \equiv 1 ( \mathrm{mod} p) \] When \( p \) is a prime number and \( p \nmid a \). ( I checked 2, 3, 5, and 7, all of these four satisfies the condition )

Note by Takeda Shigenori
3 years ago

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