I am having trouble knowing where to start to use Fermat's Little Theorem to find the least residue of 5^10 (mod 11). Could you please offer some guidance? Thanks.
Hello, you want to solve this for :
By Fermat's Little Theorem, we are left with . Now, , and , so .
Basically, you want to simplify the difficult calculation until the remaining operations can be done mentally or easily on a calculator. It is up to you to decide whether can be calculated manually.
Note that Fermat's Little Theorem is simply one particular case of Euler's Theorem :Remember though that Fermat's little Theorem only works if p is a prime number.
iff . is the Euler totient function, that is, the quantity of numbers that are coprime with . Coincidentally, if is prime, then