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National and Regional Contests
PEN Problems
PEN E Problems
7
7
Part of
PEN E Problems
Problems
(1)
E 7
Source:
5/25/2007
Show that there exists a positive integer
k
k
k
such that k \cdot 2^{n} \plus{} 1 is composite for all
n
∈
N
0
n \in \mathbb{N}_{0}
n
∈
N
0
.
modular arithmetic
Euler
pen