Problem #PRU-79651

Problems Methods Pigeonhole principle Pigeonhole principle (other) Algebra Algebraic inequalities and systems of inequalities Quadratic inequalites (several variables)
 13–14  3.0

Problem

Prove that there is a number of the form

a) 1989…19890…0 (the number 1989 is repeated several times, and then there are a few zeros), which is divisible by 1988;

b) 1988…1988, which is divisible by 1989.