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Found problems: 1

2004 Finnish National High School Mathematics Competition, 2
Tags: integrality , rational number , algebra
$a, b$ and $c$ are positive integers and \[\frac{a\sqrt{3} + b}{b\sqrt{3} + c}\] is a rational number. Show that \[\frac{a^2 + b^2 + c^2}{a + b + c}\] is an integer.