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PAMO 2022 Problem 2 - Three expressions are all squares
Source: 2022 Pan-African Mathematics Olympiad Problem 2
6/25/2022
Find all
3
3
3
-tuples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of positive integers, with
a
≥
b
≥
c
a \geq b \geq c
a
≥
b
≥
c
, such that
a
2
+
3
b
a^2 + 3b
a
2
+
3
b
,
b
2
+
3
c
b^2 + 3c
b
2
+
3
c
, and
c
2
+
3
a
c^2 + 3a
c
2
+
3
a
are all squares.
number theory
algebra
Perfect Squares