2018 · Q18
The number of all pairs (m, n), where m and n are positive integers, such that 1/m + 1/n - 1/mn = 2/5 is
Elementary MathematicsNumber System
- A6
- B5
- C4
- D2
Explanation
Clearing denominators: 5(m + n - 1) = 2mn, which rearranges to (2m - 5)(2n - 5) = 15. With m, n positive integers, 2m - 5 and 2n - 5 are positive odd factors of 15. This yields (m, n) = (3,10), (4,5), (5,4), (10,3): 4 pairs. Hence option C.