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Romania TST 2016 Day 3 P2
Romania TST 2016 Day 3 P2
Source: Romania TST 2016 Day 3 P2
November 1, 2017
number theory
Problem Statement
Given a positive integer
k
k
k
and an integer
a
≡
3
(
m
o
d
8
)
a\equiv 3 \pmod{8}
a
≡
3
(
mod
8
)
, show that
a
m
+
a
+
2
a^m+a+2
a
m
+
a
+
2
is divisible by
2
k
2^k
2
k
for some positive integer
m
m
m
.
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