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059

Part of 1965 All Russian Mathematical Olympiad

Problems(1)

ASU 059 All Russian MO 1965 first 3 digits = last 3 digits, divisible by 13

Source:

6/19/2019
A bus ticket is considered to be lucky if the sum of the first three digits equals to the sum of the last three (66 digits in Russian buses). Prove that the sum of all the lucky numbers is divisible by 1313.
number theoryDigits