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# On the treatise of determining co-primes.

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

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 $$p$$?

Note by Luke Zhang
3 years ago

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

- 3 years ago

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

- 3 years ago

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

And how did u find time during CNY?

- 3 years ago