MathDB
Bulgaria National Olympiad 1996

Source:

June 10, 2020
algebrapolynomial

Problem Statement

The quadratic polynomials ff and gg with real coefficients are such that if g(x)g(x) is an integer for some x>0x>0, then so is f(x)f(x). Prove that there exist integers m,nm,n such that f(x)=mg(x)+nf(x)=mg(x)+n for all xx.
Back to ProblemsView on AoPS