MathDB

N1

Part of 2013 Balkan MO Shortlist

Problems(1)

find a,b,c>0 when 1/a+1/b+1/c=1/p and a + b + c < 2p\sqrt{p}

Source: Balkan MO Shortlist 2013 N1 BMO

3/9/2020
Let pp be a prime number. Determine all triples (a,b,c)(a,b,c) of positive integers such that a+b+c<2ppa + b + c < 2p\sqrt{p} and 1a+1b+1c=1p\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{p}
number theoryprimereciprocal sum