Mean Value Theorems for Binary Egyptian Fractions
  In this paper, we establish two mean value theorems for the number of solutions of the Diophantine equation $\frac{a}{n}=\frac{1}{x}+\frac{1}{y}$, in the case when $a$ is fixed and $n$ varies and in the case when both $a$ and $n$ vary. 
Jing-Jing Huang and Robert C. Vaughan
math.NT