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 Proof by Tristan)

You left out a proof that there exists a solution incongruent to both 1 and 2, for those n divisible by at least two distinct prime factors.  Could you supply more details?

Posted by McWorter on 2005-09-03 21:20:24