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2017 Polish Junior Math Olympiad Finals P1

Source: 2017 Polish Junior Math Olympiad Finals

May 22, 2023

number theory

Problem Statement

Let

a

,

b

, and

c

be positive integers for which the number

\frac{a\sqrt2+b}{b\sqrt2+c}

is rational. Show that the number

ab+bc+ca

is divisible by

a+b+c

.

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