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#### bamuelsanks

##### New member

- Apr 2, 2012

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I'm rather new to number theory, and as part of an assignment I have been learning about various different primality tests.

One of these tests is the Lucas primality test.

As part of the reasoning behind the test, wikipedia states:

"If [$a^{n-1} \equiv 1 \textrm{ (mod }n\textrm{)}$] holds for a, we can deduce that a and n are coprime".

Would anybody be able to help me understand why this is true?

Thanks,

SB