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Omni-MATH / Find all positive integers a and b such that (a²+b)/(b²−a) and (b²+a)/(a²−b) are both integers.

Problem

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problem

Find all positive integers aa and bb such that a2+bb2−a\frac{a^{2}+b}{b^{2}-a} and b2+aa2−b\frac{b^{2}+a}{a^{2}-b} are both integers.
Plain-text mathematical notation (without MathML)
Find all positive integers a and b such that (a²+b)/(b²−a) and (b²+a)/(a²−b) are both integers.
Original LaTeX notation
Find all positive integers $a$ and $b$ such that $\frac{a^{2}+b}{b^{2}-a}$ and $\frac{b^{2}+a}{a^{2}-b}$ are both integers.

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Source and history

task_id
df3304a1-2a20-52c5-a114-48a50cf8382e
task_key
test--df3304a1-2a20-52c5-a114-48a50cf8382e
task_revision_id
1
config / split
/ test

Official source

initial import