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National and Regional Contests
Germany Contests
German National Olympiad
2006 German National Olympiad
1
1
Part of
2006 German National Olympiad
Problems
(1)
101...101
Source: 1st Problem 1st Day DeMO 2006
4/30/2006
Find all
n
∈
Z
+
n\in \mathbb Z^+
n
∈
Z
+
, so that
z
n
=
101
…
101
⏟
2
n
+
1
digits
z_n = \underbrace{ 101\dots101}_{2n+1 \text{ digits} }
z
n
=
2
n
+
1
digits
101
…
101
is prime.
number theory unsolved
number theory