Two Divisibility Conditions

★ 7/10Diophantine Equations number theory

Problem

Find all pairs of positive integers $(x, y)$ such that

x + y + 1 \,\mid\, 2xy \qquad\text{and}\qquad x + y - 1 \,\mid\, x^2 + y^2 - 1.

Answer

Solution

Difficulty	7/10
Topics	Diophantine Equations, number theory

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