Problem #PRU-31295

Problems Number Theory Divisibility Equations in integer numbers Methods Pigeonhole principle Pigeonhole principle (other)
 11–13  4.0

Problem

There are 100 notes of two types: \(a\) and \(b\) pounds, and \(a \neq b \pmod {101}\). Prove that you can select several bills so that the amount received (in pounds) is divisible by 101.