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Istek Lyceum Math Olympiads
Istek Lyceum Math Olympiad 2016
3
Number theory
Number theory
Source:
October 31, 2015
number theory
powers
Istek Lyceum MO
Problem Statement
Let
n
n
n
,
m
m
m
and
k
k
k
be positive integers satisfying
(
n
ā
1
)
n
(
n
+
1
)
=
m
k
.
(n-1)n(n+1)=m^k.
(
n
ā
1
)
n
(
n
+
1
)
=
m
k
.
Prove that
k
=
1.
k=1.
k
=
1.
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