MathDB

z must have a factor congruent to 3 (mod 4)

Source: Baltic Way 2005

December 28, 2010

modular arithmeticnumber theory proposednumber theory

Problem Statement

Let

x

and

y

be positive integers and assume that

z=\frac{4xy}{x+y}

is an odd integer. Prove that at least one divisor of

z

can be expressed in the form

4n-1

where

n

is a positive integer.