IMO 2016 Shortlist N8
Find all polynomials P(x) of odd degree d and with integer coefficients satisfying the following property: for each posi...
Category: Number Theory
Problem
Find all polynomials P(x) of odd degree d and with integer coefficients satisfying the following property: for each positive integer n, there exist n positive integers x1,x2,...,xn such that 1 < P(xi) P(xj) < 2 and P(xi) P(xj) is the d-th power of a rational number for every pair of indices i and j with 1 ⩽ i,j ⩽ n. Shortlisted problems 11