MathDB

Division

Source: INMO 1996 Problem 1

October 6, 2005

modular arithmeticnumber theory solvednumber theory

Problem Statement

a) Given any positive integer

n

, show that there exist distint positive integers

x

and

y

such that

x + j

divides

y + j

for

j = 1 , 2, 3, \ldots, n

; b) If for some positive integers

x

and

y

x+j

divides

y+j

for all positive integers

j

, prove that

x = y