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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
44
44
Part of
PEN A Problems
Problems
(1)
A 44
Source:
5/25/2007
Suppose that
4
n
+
2
n
+
1
4^{n}+2^{n}+1
4
n
+
2
n
+
1
is prime for some positive integer
n
n
n
. Show that
n
n
n
must be a power of
3
3
3
.
algebra
polynomial
complex numbers
Divisibility Theory