MathDB
Problems
Contests
National and Regional Contests
India Contests
India National Olympiad
1991 India National Olympiad
10
10
Part of
1991 India National Olympiad
Problems
(1)
Find s(n)
Source: INMO 1991 Problem 10
10/3/2005
For any positive integer
n
n
n
, let
s
(
n
)
s(n)
s
(
n
)
denote the number of ordered pairs
(
x
,
y
)
(x,y)
(
x
,
y
)
of positive integers for which
1
x
+
1
y
=
1
n
\dfrac{1}{x} + \dfrac{1}{y} = \dfrac{1}{n}
x
1
+
y
1
=
n
1
. Determine the set of positive integers for which
s
(
n
)
=
5
s(n) = 5
s
(
n
)
=
5