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Junior Balkan MO
2016 Junior Balkan MO
3
JBMO 2016 Problem 3
JBMO 2016 Problem 3
Source:
June 26, 2016
number theory
Problem Statement
Find all triplets of integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
such that the number
N
=
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
2
+
2
N = \frac{(a-b)(b-c)(c-a)}{2} + 2
N
=
2
(
a
−
b
)
(
b
−
c
)
(
c
−
a
)
+
2
is a power of
2016
2016
2016
.(A power of
2016
2016
2016
is an integer of form
201
6
n
2016^n
201
6
n
,where n is a non-negative integer.)
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