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2023 AMC 12A Problems/Problem 1

Revision as of 20:40, 5 November 2023 by Ms0001 (talk | contribs) (Created page with "Let <math>a</math> and <math>b</math> be positive integers such that <math>ab + 1</math> divides <math>a^{2} + b^{2}</math>. Show that <math>\frac {a^{2} + b^{2}}{ab + 1}</mat...")
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Let $a$ and $b$ be positive integers such that $ab + 1$ divides $a^{2} + b^{2}$. Show that $\frac {a^{2} + b^{2}}{ab + 1}$ is the square of an integer.

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