MathDB

2

Part of 1980 Kurschak Competition

Problems(1)

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

Source: 1980 Hungary - Kürschák Competition p2

10/9/2022
Let n>1n > 1 be an odd integer. Prove that a necessary and sufficient condition for the existence of positive integers xx and yy satisfying 4n=1x+1y\frac{4}{n}=\frac{1}{x}+\frac{1}{y} is that nn has a prime divisor of the form 4k−14k - 1.
number theory