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9
Prove that \prod^n_{k=1} k^{2k-n-1} is an integer
Prove that \prod^n_{k=1} k^{2k-n-1} is an integer
Source:
October 1, 2005
induction
number theory proposed
number theory
Problem Statement
Prove that for all positive integers
n
≥
1
n\geq 1
n
≥
1
the number
∏
k
=
1
n
k
2
k
−
n
−
1
\prod^n_{k=1} k^{2k-n-1}
∏
k
=
1
n
k
2
k
−
n
−
1
is also an integer number. Laurentiu Panaitopol.
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