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 $76$.