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2011 CIIM
Problem 2
CIIM 2011 Problem 2
CIIM 2011 Problem 2
Source:
June 9, 2016
CIIM 2011
undergraduate
Problem Statement
Let
k
k
k
be a positive integer, and let
a
a
a
be an integer such that
a
−
2
a-2
a
−
2
is a multiple of
7
7
7
and
a
6
−
1
a^6-1
a
6
−
1
is a multiple of
7
k
7^k
7
k
.Prove that
(
a
+
1
)
6
−
1
(a + 1)^6-1
(
a
+
1
)
6
−
1
is also a multiple of
7
k
7^k
7
k
.
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