When do primes and integers in modulo 2^n form equal products?

[John Creighto]

Let p1 and p2 be primes and m1 and m2 be integers when is:

When is p1^m1 mod 2^n = p2^m2 mod 2^n true?

I think this problem has applications to hash-tables.

 

[Hurkyl]

They're equal when they're equal, there really isn't much to say. I don't see what being prime has to do with it.

As an abstract Abelian group, the odd numbers with multiplication are isomorphic to the product of the group with 2 elements and the cyclic group with 2^n-2 elements.