The number of solutions of 1x+1y=16 where x,y∈N

A
9
B
18
C
21
D
28

Solution:

$\begin{array}{l} \frac{1}{x} + \frac{1}{y} = \frac{1}{6} \Rightarrow 6 (x + y) = x y \\ \Rightarrow (x - 6) (y - 6) = 36 \\ \Rightarrow (x - 6) ∣ 36 . \\ \Rightarrow x - 6 = 1, 2, 3, 4, 6, 9, 12, 18, 36 \\ \Rightarrow (x, y) = (7, 42), (8, 24), (9, 18), (10, 15), (12, 12), \\ (15, 10), (18, 9), (24, 8), (42, 7) \end{array}$

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The number of solutions of $\frac{1}{x} + \frac{1}{y} = \frac{1}{6}$ where $x, y \in N$

Solution:

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