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National and Regional Contests
PEN Problems
PEN A Problems
20
20
Part of
PEN A Problems
Problems
(1)
A 20
Source:
5/25/2007
Determine all positive integers
n
n
n
for which there exists an integer
m
m
m
such that
2
n
ā
1
2^{n}-1
2
n
ā
1
divides
m
2
+
9
m^{2}+9
m
2
+
9
.
induction
abstract algebra
modular arithmetic
quadratics
number theory
Divisibility Theory