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Mathematics
Mathematics
Problem
Let
S
(
n
)
S(n)
S
(
n
)
denote the number of ordered pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
satisfying
1
x
+
1
y
=
1
n
\frac{1}{x} + \frac{1}{y} = \frac{1}{n}
x
1
+
y
1
=
n
1
, where
n
>
1
n > 1
n
>
1
and
x
,
y
,
n
∈
N
x, y, n \in N
x
,
y
,
n
∈
N
. (i) Find the value of
S
(
6
)
S(6)
S
(
6
)
. (ii) Show that, if
n
n
n
is prime, then
S
(
n
)
=
3
S(n) = 3
S
(
n
)
=
3
, always.
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