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National and Regional Contests
Vietnam Contests
Hanoi Open Mathematics Competition
2012 Hanoi Open Mathematics Competitions
6
HOMC2012
HOMC2012
Source:
January 29, 2016
algebra
AMC
Problem Statement
For every n = 2; 3; : : : , we put
A
n
=
(
1
−
1
1
+
2
)
X
(
1
−
1
1
+
2
+
3
)
X
(
1
−
1
1
+
2
+
3
+
.
.
.
+
n
)
A_n = \left(1 - \frac{1}{1+2}\right) X \left(1 - \frac{1}{1+2+3}\right)X \left(1 - \frac{1}{1+2+3+...+n}\right)
A
n
=
(
1
−
1
+
2
1
)
X
(
1
−
1
+
2
+
3
1
)
X
(
1
−
1
+
2
+
3
+
...
+
n
1
)
Determine all positive integer n (n \geq 2) such that
1
A
n
\frac{1}{A_n}
A
n
1
is an integer.
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