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2022 Puerto Rico Team Selection Test
1
3x3 system Puerto Rico TST 2022.1.1
3x3 system Puerto Rico TST 2022.1.1
Source:
March 23, 2024
algebra
system of equations
number theory
Problem Statement
Find all triples
(
a
,
b
,
c
)
(a, b, c)
(
a
,
b
,
c
)
of positive integers such that:
a
+
b
+
c
=
24
a + b + c = 24
a
+
b
+
c
=
24
a
2
+
b
2
+
c
2
=
210
a^2 + b^2 + c^2 = 210
a
2
+
b
2
+
c
2
=
210
a
b
c
=
440
abc = 440
ab
c
=
440
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