According to this Wikipedia article, we know that an integer $n\; (\geq 2)$ is prime if and only if the polynomial congruence relation
$ (x - a)^n \equiv (x^n - a) \pmod{n} $
holds for all integers $a$ coprime to $n$ (or even just for some such integer $a$, in particular for $a = 1$).
Then the Fermat Little Theorem says, $n$ is a probable prime if
$ a^n \equiv a \pmod{n} $
Inside the article it said $x$ should never be substituted by a number, so If we do so, then for primality testing of a number like $211$ we would have something like this as an example :
$ (2 + 3)^{211} \equiv 2^{211} + 3 \pmod{n} $
So can't we use the above equation for some reduction in modular exponentiation?