# Euler's Totient Function

1. Mar 5, 2012

### squire636

I understand that for m = pq where p and q are prime numbers, $\Phi$(m) = (p-1)(q-1). Is there any way that, knowing the numerical value of m and $\Phi$(m), we could deduce p and q, the prime factors of m?

Thanks!

2. Mar 6, 2012

### squire636

Specifically, I know that a huge number m is the product of two primes and I know $\Phi$(m)...but I can't figure out which primes those are and I don't want to figure it out by brute force.

3. Mar 6, 2012

### I like Serena

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 x2 - Sx + m = 0.