Problem #PRU-79651

Problems Methods Pigeonhole principle Pigeonhole principle (other) Algebra and arithmetic Algebraic inequalities and systems of inequalities Quadratic inequalites (several variables)

Problem

Prove that there is a number of the form

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

b) \(1988 \dots 1988\), which is divisible by 1989.