Let denote the number of ordered pairs satisfying

MATHEMATICS · Multi-part · CBSE · Mathematics · Real Numbers · Real Numbers

Problem

Let

S(n)

denote the number of ordered pairs

(x, y)

satisfying

\frac{1}{x} + \frac{1}{y} = \frac{1}{n}

, where

n > 1

and

x, y, n \in N

. (i) Find the value of

S(6)

. (ii) Show that, if

n

is prime, then

S(n) = 3

, always.