Question

Find inverse of 5 modulo 23 using Fermat’s theorem

Answer 1

If I have a general modulo equation:

5x+1≡2(mod6)5x+1≡2(mod6)

What is the fastest way to solve it? My initial thought was:

5x+1≡2(mod6)5x+1≡2(mod6)⇔5x+1−1≡2−1(mod6)⇔5x+1−1≡2−1(mod6)⇔5x≡1(mod6)⇔5x≡1(mod6)

Then solve for the inverse of 55 modulo 6. Is it a right approach?