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PEN Problems
PEN N Problems
12
N 12
N 12
Source:
May 25, 2007
modular arithmetic
More Sequences
Problem Statement
The sequence
{
a
n
}
n
≥
1
\{a_{n}\}_{n \ge 1}
{
a
n
}
n
≥
1
is defined by
a
n
=
1
+
2
2
+
3
3
+
⋯
+
n
n
.
a_{n}= 1+2^{2}+3^{3}+\cdots+n^{n}.
a
n
=
1
+
2
2
+
3
3
+
⋯
+
n
n
.
Prove that there are infinitely many
n
n
n
such that
a
n
a_{n}
a
n
is composite.
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