Problem

Source: New Zealand NZMOC Camp Selection Problems 2015 p6

Tags: number theory



In many computer languages, the division operation ignores remainders. Let’s denote this operation by //, so for instance 13//3=4. If, for some b, a//b=c, then we say that c is a near factor of a. Thus, the near factors of 13 are 1, 2, 3, 4, and 6. Let a be a positive integer. Prove that every positive integer less than or equal to a is a near factor of a.