MathDB
Quotients

Source: All Russian Olympiad 2017,Day2,grade 9,P5

May 3, 2017
number theory

Problem Statement

There are n>3n>3 different natural numbers, less than (nāˆ’1)!(n-1)! For every pair of numbers Ivan divides bigest on lowest and write integer quotient (for example, 100100 divides 77 =14= 14) and write result on the paper. Prove, that not all numbers on paper are different.