MathDB
Problems
Contests
National and Regional Contests
USA Contests
USA - College-Hosted Events
Harvard-MIT Mathematics Tournament
2021 Harvard-MIT Mathematics Tournament.
1
2021 Team #1
2021 Team #1
Source:
June 27, 2021
algebra
Problem Statement
Let
a
a
a
and
b
b
b
be positive integers with
a
>
b
a>b
a
>
b
. Suppose that
a
+
b
+
a
−
b
\sqrt{\sqrt{a}+\sqrt{b}}+\sqrt{\sqrt{a}-\sqrt{b}}
a
+
b
+
a
−
b
is an integer. (a) Must
a
\sqrt{a}
a
be an integer? (b) Must
b
\sqrt{b}
b
be an integer?
Back to Problems
View on AoPS