Problem #PRU-65001

Problems Calculus Number sequences Number sequences (other) Algebra and arithmetic Number theory. Divisibility The fundamental theorm of arithmetic. Prime factorisation.

Problem

In a row there are 20 different natural numbers. The product of every two of them standing next to one another is the square of a natural number. The first number is 42. Prove that at least one of the numbers is greater than 16,000.