Euler's Totient Theorem Problem 1 Solution

Problem

(BorealBear) Find the last two digits of $7^{81}-3^{81}$ .

This is a direct application of Euler's Totient Theorem. Since $\phi(100)=40$ , this reduces to $7^1-3^1\equiv \boxed{04}\pmod{100}$ . -BorealBear