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Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
39
39
Part of
PEN A Problems
Problems
(1)
A 39
Source:
5/25/2007
Let
n
n
n
be a positive integer. Prove that the following two statements are equivalent. [*]
n
n
n
is not divisible by
4
4
4
[*] There exist
a
,
b
ā
Z
a, b \in \mathbb{Z}
a
,
b
ā
Z
such that
a
2
+
b
2
+
1
a^{2}+b^{2}+1
a
2
+
b
2
+
1
is divisible by
n
n
n
.
Divisibility Theory
pen