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Wanted : 3 quadratic polynomials such that P(x)+Q(y)=R(z).

Source: Tuymaada 2001, day 1, problem 3.

April 30, 2007

quadraticsalgebrapolynomialfunctionalgebra proposed

Problem Statement

Do there exist quadratic trinomials

P, \ \ Q, \ \ R

such that for every integers

x

and

y

an integer

z

exists satisfying

P(x)+Q(y)=R(z)?

Proposed by A. Golovanov