I have seen that there are similar question here but none that really answers the question. I understand that if I choose the 'encryption exponent e' not coprime with Φ(n) than there is not a unique way to decrypt a message. What I am wondering is what is the mathemathical reason behind this? It seems to me that since m^(kΦ(n)+1) = m mod N and d is defined as (kΦ(n)+1)/e then d*e is always going to be kΦ(n)+1 . What am I missing?