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National and Regional Contests
Moldova Contests
Chisinau City MO
1976 Chisinau City MO
120
120
Part of
1976 Chisinau City MO
Problems
(1)
Chisinau MO p120 1976 VIII product of \sqrt[m]{m}-\sqrt[k]{k}
Source:
3/16/2021
Find the product of all numbers of the form
m
m
−
k
k
\sqrt[m]{m}-\sqrt[k]{k}
m
m
−
k
k
,
m
,
k
m ,k
m
,
k
are natural numbers satisfying the inequalities
1
≤
k
<
m
≤
n
1 \le k < m \le n
1
≤
k
<
m
≤
n
, where
n
>
3
n> 3
n
>
3
.
algebra
Product
radical