2013 Mock AIME I Problems/Problem 14
Revision as of 10:51, 4 August 2024 by Thepowerful456 (talk | contribs) (more thorough explanation of why fermat works here)
Problem
Let If are its roots, then compute the remainder when is divided by 997.
Solution
By Vieta's Formulas, the product of the roots is . Since is prime with , all the roots are relatively prime to . Thus, by Fermat's Little Theorem, we have , which, by Vieta, equals . Thus our answer is .