olymmath

OSN 2008 Problem 3

  • Day 1

Find all natural number which can be expressed in a+bc+b+ca+c+ab\frac{a+b}{c}+\frac{b+c}{a}+\frac{c+a}{b} where a,b,c∈Na,b,c\in \mathbb{N} satisfy gcd⁡(a,b)=gcd⁡(b,c)=gcd⁡(c,a)=1\gcd(a,b)=\gcd(b,c)=\gcd(c,a)=1

Dataset text AI-MO AoPS. Quoted with source.

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