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National and Regional Contests
PEN Problems
PEN O Problems
17
17
Part of
PEN O Problems
Problems
(1)
O 17
Source:
5/25/2007
Find the maximum number of pairwise disjoint sets of the form
S
a
,
b
=
{
n
2
+
a
n
+
b
∣
n
∈
Z
}
,
S_{a,b}=\{n^{2}+an+b \; \vert \; n \in \mathbb{Z}\},
S
a
,
b
=
{
n
2
+
an
+
b
∣
n
∈
Z
}
,
with
a
,
b
∈
Z
a,b \in \mathbb{Z}
a
,
b
∈
Z
.