MathDB

International Zhautykov Olympiad 2011 - Problem 3

Source:

January 16, 2011

modular arithmeticlogarithmsinductionnumber theory unsolvednumber theory

Problem Statement

Let

\mathbb{N}

denote the set of all positive integers. An ordered pair

(a;b)

of numbers

a,b\in\mathbb{N}

is called interesting, if for any

n\in\mathbb{N}

there exists

k\in\mathbb{N}

such that the number

a^k+b

is divisible by

2^n

. Find all interesting ordered pairs of numbers.