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1/n=1/x(x+1)+\1/(x+1)(x+2 }+...+1/y(y+1), with x,y integers

Source: Mathematics Regional Olympiad of Mexico West 2019 P5

September 9, 2022

number theoryDiophantine equation

Problem Statement

Prove that for every integer

n > 1

there exist integers

x

and

y

such that

\frac{1}{n}=\frac{1}{x(x+1)}+\frac{1}{(x+1)(x+2)}+...+\frac{1}{y(y+1)}.