Congruence and Modular Arithmetic

FLT actually follows from the more general

Fermat’s Little Theorem (F$l$T)

For all prime numbers $p$ and integers $a$ not divisible by $p$, we have $a^{p-1}\equiv 1(\mathrm{mod}p)$

Corollary for Fermat’s Little Theorem

$a^p\equiv a(\mathrm{mod}p)$

“Fermat’s Little Theorem gives $a^{(p-1)}\equiv a(\mathrm{mod}p)$ if gcd(a, p)=1, where p is a prime. Therefore, we can calculate the modular inverse of a as a^(p-2), by fast exponentiation also.”