MathDB
Sum of any 3 sides of a quad div by 4th=>some 2 are equal

Source: RMO (Mumbai Region) 2015 P8

December 6, 2015
inequalitiesnumber theorygeometrygeometry proposed

Problem Statement

The length of each side of a convex quadrilateral ABCDABCD is a positive integer. If the sum of the lengths of any three sides is divisible by the length of the remaining side then prove that some two sides of the quadrilateral have the same length.