Let p be an odd prime. Prove that the quadratic congruence has a solution if and only if . (hint: use Wilson's theorem)
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Wilson's theorem states that . Since we can regroup the terms in the product in pairs, as .
Can you take it from there?
Alright, I have the <= direction.
For the => direction, i have worked with wilson's down to where but can't quite see how to get to the required conclusion of
Well if and for then we always must have . What can you say about the order of mod if ?
Last edited by Bruno J.; March 5th 2010 at 11:17 PM.
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