MathDB
Problems
Contests
National and Regional Contests
Albania Contests
Albania Team Selection Test
2013 Albania Team Selection Test
5
5
Part of
2013 Albania Team Selection Test
Problems
(1)
Find the couples
Source: Albania IMO TST 2013
5/25/2013
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
abstract algebra
number theory unsolved
number theory