Hi, I understand that the gcd of those numbers is 1. However, I don't quite understand your hint about the euler phi function, because my teacher hardly taught this. If you could help me understand it that would be great
Hi, I understand that the gcd of those numbers is 1. However, I don't quite understand your hint about the euler phi function, because my teacher hardly taught this. If you could help me understand it that would be great
Euler's theorem states that if $\displaystyle (a,n)=1$ then $\displaystyle a^{\phi(n)}\equiv 1\text{ mod }n$. So, since $\displaystyle (5,99)=1$ we see that $\displaystyle 5^{183}=5^{3+3\cdot 60}=5^3\cdot \left(5^{\phi(99)}\right)^3\equiv 5^3\text{ mod }99$