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2024 CMIMC
2024 CMIMC Algebra and Number Theory
6
6
Part of
2024 CMIMC Algebra and Number Theory
Problems
(1)
2024 Alg/NT Problem 6
Source:
4/14/2024
Integers
a
,
b
a, b
a
,
b
satisfy the following property: the line
y
=
2
x
+
a
b
y = 2x + ab
y
=
2
x
+
ab
passes through all intersection points of the two parabolas given by y = x^2 + 2x + a, y = 2x^2 +bx, which intersect at least once. How many such
(
a
,
b
)
(a, b)
(
a
,
b
)
satisfy
∣
a
b
∣
≤
100
|ab| \leq 100
∣
ab
∣
≤
100
?Proposed by Justin Hsieh
algebra