MathDB

Nice NT with powers of two

Source: Romania TST 2024 Day 1 P3

July 31, 2024

number theoryDivisibility

Problem Statement

Let

n{}

be a positive integer and let

a{}

and

b{}

be positive integers congruent to 1 modulo 4. Prove that there exists a positive integer

k{}

such that at least one of the numbers

a^k-b

and

b^k-a

is divisible by

2^n.

Cătălin Liviu Gherghe