Perfect square preserving polynomial
Source: Iran TST 2008
May 25, 2008
algebrapolynomialfunctionlimitsearchnumber theoryrelatively prime
Problem Statement
Find all polynomials of one variable with integer coefficients such that if and are natural numbers such that a \plus{} b is a perfect square, then p\left(a\right) \plus{} p\left(b\right) is also a perfect square.