Ternary Egyptian fractions with prime denominator

Adva Mond, Julien Portier

For a prime number $p$, let $A_3(p)=|\{m\in \mathbb{N}:\exists m_1,m_2,m_3\in \mathbb{N},\frac{m}{p}=\frac{1}{m_1}+\frac{1}{m_2}+\frac{1}{m_3}\}|$. In 2019 Luca and Pappal…