MathDB
Quadratic equation two integer solution for (a-b)^2<=8sqrt(ab)

Source: 2003 Korea Junior Math Olympiad

June 28, 2024
Integerquadratics equationalgebranumber theoryquadratics

Problem Statement

a,ba, b are odd numbers that satisfy (a−b)2≤8ab(a-b)^2 \le 8\sqrt {ab}. For n=abn=ab, show that the equation x2−2([n]+1)x+n=0x^2-2([\sqrt n]+1)x+n=0 has two integral solutions. [r][r] denotes the biggest integer, not strictly bigger than rr.
Back to ProblemsView on AoPS