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 data-equation="1">\(1\). This theorem does show to be true for all prime numbers however, it is not only true for prime numbers. There are special cases where the theorem works fro a number that is not prime, if the theorem happens to satisfy the non-prime number the number is known as a pseudoprime. Let's see an example: if we have \(4^{14}\equiv1\) (mod \(15\)), we can see that the number \(15\) is not prime because it is divisible by \(3\) and \(5\), next we want to see if the statement is true. Let's write \(4^{14}\) as \(\left(4^2\right)^7\) \(\equiv1\) (mod \(15\)). We can see that we will have \(16\) (mod \(15\)), giving us a remainder of 1 therefore, we can raise \(1^7\) and get that the remainder is \(1\) making our statement true, the number \(15\) is in fact a pseudoprime because it satisfies Fermat's theorem without being a prime number.