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PEN A Problems
55
A 55
A 55
Source:
May 25, 2007
Divisibility Theory
Problem Statement
Show that for every natural number
n
n
n
the product
(
4
−
2
1
)
(
4
−
2
2
)
(
4
−
2
3
)
⋯
(
4
−
2
n
)
\left( 4-\frac{2}{1}\right) \left( 4-\frac{2}{2}\right) \left( 4-\frac{2}{3}\right) \cdots \left( 4-\frac{2}{n}\right)
(
4
−
1
2
)
(
4
−
2
2
)
(
4
−
3
2
)
⋯
(
4
−
n
2
)
is an integer.
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