The quadratic equation x^2-3x+2=0 has the "correct" number of solutions modulo 5 and 7. However, modulo 6 the equation has four solutions; namely, 1, 2, 4, and 5. For what positive integers n does the equation x^2-3x+2=0 have exactly two incongruent solutions modulo n?

(In reply to I think the answer is... by KC)

For x=0,1,2,3 we have x² -3x + 2 = 2,0,0,2 resp. So there are only 2 solutions mod 4, and 4 is not a prime. Your conjecture needs to be amended, I'm afraid.

Posted by Richard on 2005-09-03 17:52:56