Mathegoras

Number theory › Divisibility › Assorted divisibility puzzles

Least n with many unit-fraction solutions

High school · ●●●○○ 50 pts

Let xx, yy and nn be positive integers, and count the solutions (x,y)(x, y) of 1x+1y=1n\frac{1}{x}+\frac{1}{y}=\frac{1}{n} with x≤yx \le y. For n=4n=4 there are exactly three such solutions. Find the least value of nn for which the number of solutions exceeds one thousand.

Sign in to save your progress.

Diophantine equationsunit fractionsdivisor countingprime factorisation