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-   -   Euler's Totient Function (http://www.physicsforums.com/showthread.php?t=584239)

 squire636 Mar5-12 11:46 PM

Euler's Totient Function

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!

 squire636 Mar6-12 12:01 AM

Re: Euler's Totient Function

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.

 I like Serena Mar6-12 01:05 AM

Re: Euler's Totient Function

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.

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