MathDB
Rational, then Integer

Source: Indonesia Mathematics Olympiad 2005 Day 1 Problem 3

June 2, 2008
number theory proposednumber theory

Problem Statement

Let k k and m m be positive integers such that \displaystyle\frac12\left(\sqrt{k\plus{}4\sqrt{m}}\minus{}\sqrt{k}\right) is an integer. (a) Prove that k \sqrt{k} is rational. (b) Prove that k \sqrt{k} is a positive integer.
Back to ProblemsView on AoPS