PowerMod Is Eventually Periodic

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The sequence is known to be eventually periodic, which is to say that there is a smallest positive such that for all . Naturally we call the period, and the minimal value of , the periodicity onset. L. Euler proved that the period must divide the totient of the modulus .

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In case of coprime and , the onset is zero.

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Contributed by: Oleksandr Pavlyk (December 2008)
Open content licensed under CC BY-NC-SA


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