In order to solve an ElGamal cryptographic problem, I need to solve
8x≡1 (mod 17)
Or simply, find the inverse of 8 in the context of modular 17.
By the Extended Euclidean Algorithm, we get:
17=8(2)+1 => 1=17-8(2)
So, simply, the inverse of 8 (mod 17) should be 2, but this is not the case, It is indeed 15. What am I missing here? My experience with number theory is touchy, and this code theory course requires it.