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2020 CIIM
2
Cubic and Quadratic
Cubic and Quadratic
Source: CIIM 2020 P2
October 26, 2020
number theory
algebra
Problem Statement
Find all triples of positive integers
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
such that the following equations are both true: I-
a
2
+
b
2
=
c
2
a^2+b^2=c^2
a
2
+
b
2
=
c
2
II-
a
3
+
b
3
+
1
=
(
c
ā
1
)
3
a^3+b^3+1=(c-1)^3
a
3
+
b
3
+
1
=
(
c
ā
1
)
3
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