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1999 Ukraine National Mathematical Olympiad
Problem 6
k^L/L^k=k!/L!
k^L/L^k=k!/L!
Source: Ukraine 1999 Grade 9 P6
May 10, 2021
number theory
Diophantine equation
Problem Statement
Find all pairs
(
k
,
l
)
(k,l)
(
k
,
l
)
of positive integers such that
k
l
l
k
=
k
!
l
!
\frac{k^l}{l^k}=\frac{k!}{l!}
l
k
k
l
ā
=
l
!
k
!
ā
.
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