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2^{2n} + 2^n + 5 divisible by 5 (HOMC 2010 J Q2)
2^{2n} + 2^n + 5 divisible by 5 (HOMC 2010 J Q2)
Source:
July 25, 2019
number theory
divisible
Problem Statement
Find the number of integer
n
n
n
from the set
{
2000
,
2001
,
.
.
.
,
2010
}
\{2000,2001,...,2010\}
{
2000
,
2001
,
...
,
2010
}
such that
2
2
n
+
2
n
+
5
2^{2n} + 2^n + 5
2
2
n
+
2
n
+
5
is divisible by
7
7
7
(A):
0
0
0
, (B):
1
1
1
, (C):
2
2
2
, (D):
3
3
3
, (E) None of the above.
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