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National and Regional Contests
PEN Problems
PEN A Problems
17
17
Part of
PEN A Problems
Problems
(1)
A 17
Source:
5/25/2007
Let
m
m
m
and
n
n
n
be natural numbers such that
A
=
(
m
+
3
)
n
+
1
3
m
A=\frac{(m+3)^{n}+1}{3m}
A
=
3
m
(
m
+
3
)
n
+
1
is an integer. Prove that
A
A
A
is odd.
modular arithmetic
quadratics
number theory
relatively prime
Divisibility Theory
pen