If a and N coprime, a < N and r is even how can a^(r) = 1 mod(N) be written as a^(r) - 1 = 0 mod(N) ? I don't know much number theory (I'm a physics student) Thanks
Hi, the conditions you list at the start don't matter for what you've just asked (a, N coprime, etc). For any a,b, and N, a=b mod (N) if and only if N divides a-b if and only if N divides (a-b)-0 if and only if a-b=0 mod(N) Working mod N you can add, subtract and multiply as normal (division isn't always possible!), you just have the luxury of reducing things mod(N) afterwards.