Problem #PRU-79488

Problems Methods Pigeonhole principle Pigeonhole principle (other) Algebra and arithmetic Number theory. Divisibility The fundamental theorm of arithmetic. Prime factorisation.
 13–15  4.0

Problem

The product of 1986 natural numbers has exactly 1985 different prime factors. Prove that either one of these natural numbers, or the product of several of them, is the square of a natural number.