I understand that for m = pq where p and q are prime numbers, [itex]\Phi[/itex](m) = (p-1)(q-1). Is there any way that, knowing the numerical value of m and [itex]\Phi[/itex](m), we could deduce p and q, the prime factors of m? Thanks!
Specifically, I know that a huge number m is the product of two primes and I know [itex]\Phi[/itex](m)...but I can't figure out which primes those are and I don't want to figure it out by brute force.
If you know m=pq and Φ=(p-1)(q-1), then define S=m-Φ+1=p+q. So you have the product m and the sum S. That means p and q are the solutions of the quadratic x^{2} - Sx + m = 0.