MathDB

1/n =1/x +1/y , b has a prime divisor of form 4k-1

Source: 1980 Hungary - Kürschák Competition p2

October 9, 2022

number theory

Problem Statement

Let

n > 1

be an odd integer. Prove that a necessary and sufficient condition for the existence of positive integers

x

and

y

satisfying

\frac{4}{n}=\frac{1}{x}+\frac{1}{y}

is that

n

has a prime divisor of the form

4k - 1