Use Fermat's Little Theorem
4972
Mod of numbers with large exponents [modular order reduction]
157131
Show that all Fermat numbers pass the base $2$ test (pseudoprime).
32343
Converse to Chinese Remainder Theorem
69228
Factorial of 0 - a convenience?
137175
Fermat's little theorem proof by Euler
5043
Show that $2^n>1+n\sqrt{2^{n-1}}$
60349
Schur's theorem and numbers
151636
Fast way to calculate n! mod m where m is prime?
20574
Understanding the proof for $\gcd (F_n, F_{n+k}) = 1$ where $F_n$ is a Fermat number
47060
Split $n$ into nontrivial factors via a nontrivial square-root of $1\!\pmod{\!n}$
1189
Using Fermats prime numbers to prove that there is infinitely many prime numbers
21629
Using Fermat's Little Theorem Prove if $p$ is prime, prove $1^p + 2^p + 3^p +...+(p-1)^p \equiv 0 \bmod{p}$
157652
Fermat's Last Theorem for Gaussian Integers (excluding the integers or  same pure imaginaries)
78188
How can I get the smallest possible answer with the Chinese Remainder Theorem?
41641
$(n-7)(n+7)=$ some perfect square
136894
Reference request: Clean proof of Fermat's last theorem for $n=3$.
4140
Fermat's Last Theorem with negative exponent