*Credit for this problem goes to Peter Macko*.

If $n$ is a positive integer, prove that $(2^n)! $ is divisible by $2^{2^n-1}$ and that its quotient is an odd number.

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## Saturday, January 9, 2010

###
Factorial and power of 2

*Credit for this problem goes to Peter Macko*.

If $n$ is a positive integer, prove that $(2^n)! $ is divisible by $2^{2^n-1}$ and that its quotient is an odd number.
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Math is evil...

If $n$ is a positive integer, prove that $(2^n)! $ is divisible by $2^{2^n-1}$ and that its quotient is an odd number.

Labels:
divisibility,
factorial,
Number Theory,
power of two

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