MathDB
Polynomial with integer coefficients

Source: 2013 Baltic Way, Problem 2

December 30, 2013
algebrapolynomial

Problem Statement

Let kk and nn be positive integers and let x1,x2,⋯ ,xk,y1,y2,⋯ ,ynx_1, x_2, \cdots, x_k, y_1, y_2, \cdots, y_n be distinct integers. A polynomial PP with integer coefficients satisfies P(x1)=P(x2)=⋯=P(xk)=54P(x_1)=P(x_2)= \cdots = P(x_k)=54 P(y1)=P(y2)=⋯=P(yn)=2013.P(y_1)=P(y_2)= \cdots = P(y_n)=2013.
Determine the maximal value of knkn.
Back to ProblemsView on AoPS