MathDB
1+2n+3n^2+...+(p-1)n^(p-2), F(a)!=F(b) mod p

Source: Putnam 1983 A3

September 14, 2021
number theory

Problem Statement

Let pp be an odd prime and let F(n)=1+2n+3n2+…+(p−1)np−2.F(n)=1+2n+3n^2+\ldots+(p-1)n^{p-2}.Prove that if aa and bb are distinct integers in {0,1,2,…,p−1}\{0,1,2,\ldots,p-1\} then F(a)F(a) and F(b)F(b) are not congruent modulo pp.
Back to ProblemsView on AoPS