Problem
ALG-B1-M09-P014 Egyptian fraction
#14
★★★☆☆ Level 3 of 5
Find positive integer solutions of \(\frac{1}{x}+\frac{1}{y}=\frac{1}{6}\).
Multiply by \(6xy\) and complete to a product.
We get \(6x+6y=xy\), so \(xy-6x-6y=0\). Thus \((x-6)(y-6)=36\). Checking positive divisors of \(36\), we obtain \((x,y)=(7,42),(8,24),(9,18),(10,15),(12,12)\) and the symmetric pairs.
A very useful template for fractional Diophantine equations.