Either you find the multiplicative inverse of modulo 7, that is a such that (you can see that a=2)
Either you use Fermat's little theorem :
This is my first post. I am practicing simple congruence theory to solve divisibility problems.
For example, to show :
, which is what we set out to prove.
This works very well for all the problems I've been working on, but there is one with a minus sign that is throwing me off:
If you had to deal modulo n, where n is not necessarily prime, use Euler's theorem (Euler's theorem - Wikipedia, the free encyclopedia)
Otherwise, in order to find the multiplicative inverse of a number modulo n (which exists if this number is coprime with n), use trial and error or (better ) the extended Euclidean algorithm (Extended Euclidean algorithm - Wikipedia, the free encyclopedia)