A 12-digit positive integer consisting only of digits 1,5 and 9 is divisible by 37. Prove that the sum of its digits is not equal to 76.
Source: Baltic Way 2006
Tags: modular arithmetic, number theory proposed, number theory
A 12-digit positive integer consisting only of digits 1,5 and 9 is divisible by 37. Prove that the sum of its digits is not equal to 76.