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5
Find the couples
Find the couples
Source: Albania IMO TST 2013
May 25, 2013
abstract algebra
number theory unsolved
number theory
Problem Statement
Let
k
k
k
be a natural number.Find all the couples of natural numbers
(
n
,
m
)
(n,m)
(
n
,
m
)
such that :
(
2
k
)
!
=
2
n
ā
m
(2^k)!=2^n*m
(
2
k
)!
=
2
n
ā
m
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