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2020 ASDAN Math Tournament
15
2020 Team #15
2020 Team #15
Source:
October 24, 2023
team test
Problem Statement
For integers
z
z
z
, let
#
(
z
)
\#(z)
#
(
z
)
denote the number of integer ordered pairs
(
x
,
y
)
(x, y)
(
x
,
y
)
that satisfy
x
2
−
x
y
+
y
2
=
z
x^2 - xy + y^2 = z
x
2
−
x
y
+
y
2
=
z
. How many integers
z
z
z
between
0
0
0
and
150
150
150
inclusive satisfy
#
(
z
)
≡
6
\#(z) \equiv 6
#
(
z
)
≡
6
(mod
12
12
12
)?
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