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Baltic Way
2012 Baltic Way
16
16
Part of
2012 Baltic Way
Problems
(1)
Product of Three Consecutive Integers
Source: 2012 Baltic Way, Problem 16
11/22/2012
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
.
number theory unsolved
number theory