For any two positive integers n>m prove the following inequality: [m,n]+[m+1,n+1]≥2nm√m−nAs always, [x,y] means the least common multiply of x,y. Proposed by A. Golovanov
Problem
Source: St. Petersburg MO 2001, 11th grade, P4
Tags: inequalities, number theory, greatest common divisor, algebra, GCD, least common multiple