MathDB
Problems
Contests
National and Regional Contests
Netherlands Contests
Dutch BxMO/EGMO TST
2010 Dutch BxMO TST
3
3
Part of
2010 Dutch BxMO TST
Problems
(1)
Number of 5-tuples.
Source:
5/25/2011
Let
N
N
N
be the number of ordered 5-tuples
(
a
1
,
a
2
,
a
3
,
a
4
,
a
5
)
(a_{1}, a_{2}, a_{3}, a_{4}, a_{5})
(
a
1
,
a
2
,
a
3
,
a
4
,
a
5
)
of positive integers satisfying
1
a
1
+
1
a
2
+
1
a
3
+
1
a
4
+
1
a
5
=
1
\frac{1}{a_{1}}+\frac{1}{a_{2}}+\frac{1}{a_{3}}+\frac{1}{a_{4}}+\frac{1}{a_{5}}=1
a
1
1
+
a
2
1
+
a
3
1
+
a
4
1
+
a
5
1
=
1
Is
N
N
N
even or odd?Oh and HINTS ONLY, please do not give full solutions. Thanks.
number theory unsolved
number theory