MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2004 Harvard-MIT Mathematics Tournament
3
2004 General, part 2 #3
2004 General, part 2 #3
Source:
March 8, 2024
number theory
algebra
Problem Statement
How many ordered pairs of integers
(
a
,
b
)
(a, b)
(
a
,
b
)
satisfy all of the following inequalities?
a
2
+
b
2
<
16
a^2 + b^2 < 16
a
2
+
b
2
<
16
a
2
+
b
2
<
8
a
a^2 + b^2 < 8a
a
2
+
b
2
<
8
a
a
2
+
b
2
<
8
b
a^2 + b^2 < 8b
a
2
+
b
2
<
8
b
Back to Problems
View on AoPS