MathNet 2018-part-03 — 181 problems (EN–VI) Question 71

How many quadruples of positive integers $(a, b, x, y)$ are there such that $x+y=a \cdot b$ and $a+b=x \cdot y$?

(A) 1
(B) 5
(C) 9
(D) 17
(E) Infinitely many