Problem #PRU-73727

Problems 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.