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National and Regional Contests
PEN Problems
PEN E Problems
8
E 8
E 8
Source:
May 25, 2007
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Problem Statement
Show that for all integer
k
>
1
k>1
k
>
1
, there are infinitely many natural numbers
n
n
n
such that
k
ā
2
2
n
+
1
k \cdot 2^{2^n} + 1
k
ā
2
2
n
+
1
is composite.
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