MathDB
Problems
Contests
International Contests
Baltic Way
2012 Baltic Way
16
Product of Three Consecutive Integers
Product of Three Consecutive Integers
Source: 2012 Baltic Way, Problem 16
November 22, 2012
number theory unsolved
number theory
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
.
Back to Problems
View on AoPS