MathDB

A=b

Source: Taiwan 1st TST 2006, 1st day, problem 3

March 29, 2006

modular arithmeticnumber theoryDivisibilityIMO ShortlistChinese Remainder TheoremHi

Problem Statement

Let

a

b

be positive integers such that

b^n+n

is a multiple of

a^n+n

for all positive integers

n

. Prove that

a=b

.
Proposed by Mohsen Jamali, Iran