Problem #PRU-73727

Problems Algebra and arithmetic Number theory. Divisibility Divisibility of a number. General properties Geometry Solid geometry Lines and planes in space Methods Pigeonhole principle Pigeonhole principle (other)
 12–14  4.0

Problem

Out of the given numbers 1, 2, 3, ..., 1000, find the largest number \(m\) that has this property: no matter which \(m\) of these numbers you delete, among the remaining \(1000 - m\) numbers there are two, of which one is divisible by the other.