MathDB
cd | (a+b)^2 any permutation a,b,c,d

Source: All-Russian MO 1999

December 31, 2012
modular arithmeticnumber theory unsolvednumber theory

Problem Statement

Four natural numbers are such that the square of the sum of any two of them is divisible by the product of the other two numbers. Prove that at least three of these numbers are equal.