Fermat's Little Theorem states, if \(p\) is a prime number and \(a\) is an integer, \(a^p\equiv a\) (mod \(p\)). The theorem itself is used and is very helpful when testing numbers to see of if  they are not prime. It can be easy to see whether a small number is not prime however, with Fermat's Theorem it is very fast.  One of the most important things to note is that the theorem does not tell whether a number is prime but it will tell you if it is not prime. Therefore, the famous theorem also states that if \(p\) does not divide \(a\), then \(a^{p-1}\equiv\) \(1\) (mod \(p\)).