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number of solutions of a diophantine

Source: Romanian District Olympiad 2015, Grade VIII, Problem 3

September 25, 2018
Diophantine equationalgebra

Problem Statement

Find #{(x,y)∈N2∣1x−1y=12016}, \#\left\{ (x,y)\in\mathbb{N}^2\bigg| \frac{1}{\sqrt{x}} -\frac{1}{\sqrt{y}} =\frac{1}{2016}\right\} , where #A \# A is the cardinal of A. A .
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