MathDB
P in Q[x] a polynomial of degree 2016, m = n^3 + 3n + 1$

Source: 2016 Saudi Arabia IMO TST , level 4+, III p3

July 29, 2020
algebrapolynomialarithmetic sequence

Problem Statement

Let P∈Q[x]P \in Q[x] be a polynomial of degree 20162016 whose leading coefficient is 11. A positive integer mm is nice if there exists some positive integer nn such that m=n3+3n+1m = n^3 + 3n + 1. Suppose that there exist infinitely many positive integers nn such that P(n)P(n) are nice. Prove that there exists an arithmetic sequence (nk)(n_k) of arbitrary length such that P(nk)P(n_k) are all nice for k=1,2,3k = 1,2, 3,
Back to ProblemsView on AoPS