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Definition (Coprime)
Given a,b∈Za,b\in\mathbb{Z}a,b∈Z such that gcd(a,b)=1gcd(a,b)=1gcd(a,b)=1 then we say aaa and bbb are coprime.
Theorem (Fermat’s little theorem)
If ppp is prime, and aaa is coprime to ppp (i.e. (p,a)=1(p,a)=1(p,a)=1) then ap−1≡1(modp)a^{p-1}\equiv 1 \pmod{p}ap−1≡1(modp)
Arithmetic Function
Chinese Remainder Theorem
Coprime
Pythagorean Triple
The Set of Residue Classes mod p
Jacobi Symbol
Legendre Symbol