\(gcd(k,p)=1\)

The formula states:

\({ k }^{ p\quad }\equiv \quad k-p\quad (mod\quad p)\)

\(k>p\)

For example:

Using \(2\) as \(p\),

And knowing that \(k=3\)

\({ 3 }^{ 2 }\quad \equiv \quad 1\quad (mod\quad 2)\)

By trying out other primes, this always work.

However, one link is still missing can we solve this equation by only knowing \(p\)?

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## Comments

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TopNewestIt doesnt only work for primes, it works for some other numbers too, but I'm not sure how to generalize it

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This has been proven using Fermat's Little theorem. But how do I validate it?

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Did u proof that it would work for all primes and only primes?

And how did u find time during CNY?

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