Show that if and doesn't divide then there is at least one prime

factor of such that .

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- November 9th 2009, 07:52 PMcomssaCongruence proof
Show that if and doesn't divide then there is at least one prime

factor of such that . - November 9th 2009, 09:10 PMtonio
- November 10th 2009, 11:03 AMcomssa

so

How would you link p and q together so that q divides (p-1)? Thanks.

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Edit:

Would this be a good proof?

Using

because otherwise , which contradicts with the given conditions.

for some i between 0 and n because it is the only possible way that p divides but not m.

If q is a factor of m, then we can let q be for some i between 0 and n.

since , then we can substitute with q to get

, which can be expressed as