MathDB

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

March 9, 2020

number theoryprimereciprocal sum

Problem Statement

Let

p

be a prime number. Determine all triples

(a,b,c)

of positive integers such that

a + b + c < 2p\sqrt{p}

and

\frac{1}{a}+\frac{1}{b}+\frac{1}{c}=\frac{1}{p}