Abstract
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 Pappalardi proved that x (log x)^3 ll sum _{p le x} A_{3}(p) ll x (log x)^5. We improve the upper bound, showing sum _{p le x} A_{3}(p) ll x (log x)^3 (log log x)^2.
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