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sum of all six-digit balanced numbers is divisible by 13

Source: Flanders Math Olympiad 2013 p1

December 24, 2022
number theoryDigitsdivisibleSum

Problem Statement

A six-digit number is balanced when all digits are different from zero and the sum of the first three digits is equal to the sum of the last three digits. Prove that the sum of all six-digit balanced numbers is divisible by 1313.