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Putnam
2010 Putnam
A4
A4
Part of
2010 Putnam
Problems
(1)
Putnam 2010 A4
Source:
12/6/2010
Prove that for each positive integer
n
,
n,
n
,
the number
1
0
1
0
1
0
n
+
1
0
1
0
n
+
1
0
n
ā
1
10^{10^{10^n}}+10^{10^n}+10^n-1
1
0
1
0
1
0
n
+
1
0
1
0
n
+
1
0
n
ā
1
is not prime.
Putnam
modular arithmetic
number theory
greatest common divisor
logarithms
college contests
Putnam number theory