MathDB
Equivalent polynomials

Source: Indian Team Selection Test 2015 Day 1 Problem 2

July 11, 2015
algebrapolynomial

Problem Statement

Let ff and gg be two polynomials with integer coefficients such that the leading coefficients of both the polynomials are positive. Suppose deg⁡(f)\deg(f) is odd and the sets {f(a)∣a∈Z}\{f(a)\mid a\in \mathbb{Z}\} and {g(a)∣a∈Z}\{g(a)\mid a\in \mathbb{Z}\} are the same. Prove that there exists an integer kk such that g(x)=f(x+k)g(x)=f(x+k).
Back to ProblemsView on AoPS