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Caucasus Mathematical Olympiad
2021 Caucasus Mathematical Olympiad
1
On a^2+b=c^2
On a^2+b=c^2
Source: VI Caucasus Mathematical Olympiad
March 14, 2021
algebra
Caucasus
value
Problem Statement
Let
a
a
a
,
b
b
b
,
c
c
c
be real numbers such that
a
2
+
b
=
c
2
a^2+b=c^2
a
2
+
b
=
c
2
,
b
2
+
c
=
a
2
b^2+c=a^2
b
2
+
c
=
a
2
,
c
2
+
a
=
b
2
c^2+a=b^2
c
2
+
a
=
b
2
. Find all possible values of
a
b
c
abc
ab
c
.
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