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Misc. 3
2018 PUMaC Live Round Miscellaneous 3
2018 PUMaC Live Round Miscellaneous 3
Source:
January 13, 2019
PuMAC
Live Round
Problem Statement
Suppose
x
,
y
∈
Z
x,y\in\mathbb{Z}
x
,
y
∈
Z
satisfy
y
4
+
4
y
3
+
28
y
+
8
x
3
+
6
y
2
+
32
x
+
1
=
(
x
2
−
y
2
)
(
x
2
+
y
2
+
24
)
.
y^4+4y^3+28y+8x^3+6y^2+32x+1=(x^2-y^2)(x^2+y^2+24).
y
4
+
4
y
3
+
28
y
+
8
x
3
+
6
y
2
+
32
x
+
1
=
(
x
2
−
y
2
)
(
x
2
+
y
2
+
24
)
.
Find the sum of all possible values of
∣
x
y
∣
|xy|
∣
x
y
∣
.
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