Problem #PRU-100704

Problems Algebra Number theory. Divisibility Division with remainders. Arithmetic of remainders Division with remainder

Problem

Seven robbers are dividing a bag of coins of various denominations. It turned out that the sum could not be divided equally between them, but if any coin is set aside, the rest could be divided so that every robber would get an equal part. Prove that the bag cannot contain \(100\) coins.