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2024 CMIMC Algebra and Number Theory
3
2024 Alg/NT Problem 3
2024 Alg/NT Problem 3
Source:
April 14, 2024
algebra
Problem Statement
The positive integer
8833
8833
8833
has the property that
8833
=
8
8
2
+
3
3
2
.
8833 = 88^2 + 33^2.
8833
=
8
8
2
+
3
3
2
.
Find the (unique) other four-digit positive integer
a
b
c
d
‾
\overline{abcd}
ab
c
d
where
a
b
c
d
‾
=
(
a
b
‾
)
2
+
(
c
d
‾
)
2
.
\overline{abcd} = (\overline{ab})^2 + (\overline{cd})^2.
ab
c
d
=
(
ab
)
2
+
(
c
d
)
2
.
Proposed by Allen Yang
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