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?

For powers of a single prime, the equation x^3-3x+2=0 have two incongruent solutions in modulo n.

Posted by K Sengupta on 2023-07-28 01:26:34