$\frac{1}{a} + \frac{1}{b} = \frac{1}{7}$, a, b ∈ N.
$\frac{1}{b} = \frac{1}{7} - \frac{1}{a}$
$\frac{1}{b} = \frac{a - 7}{7}$
$b = \frac{7a}{a - 7} = \frac{7(a - 7) + 49}{a - 7} = 7 + \frac{49}{a - 7}$
b ∈ N, значит:
a − 7 = {1; 7; 49}
a − 7 = 1
a = 8
$b = 7 + \frac{49}{8 - 7} = 7 + 49 = 56$
 
a − 7 = 7
a = 14
$b = 7 + \frac{49}{14 - 7} = 7 + 7 = 14$
 
a − 7 = 49
a = 56
$b = 7 + \frac{49}{56 - 7} = 7 + 1 = 8$
Ответ: {(8;56),(14;14),(56;8)}.