MathDB

5

Part of 2019 Regional Olympiad of Mexico West

Problems(1)

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

9/9/2022
Prove that for every integer n>1n > 1 there exist integers xx and yy such that 1n=1x(x+1)+1(x+1)(x+2)+...+1y(y+1).\frac{1}{n}=\frac{1}{x(x+1)}+\frac{1}{(x+1)(x+2)}+...+\frac{1}{y(y+1)}.
number theoryDiophantine equation