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2019-IMOC
A3
system of equations with 2019th root
system of equations with 2019th root
Source: IMOC 2019 A3
August 18, 2021
algebra
system of equations
Problem Statement
Find all
3
3
3
-tuples of positive reals
(
a
,
b
,
c
)
(a,b,c)
(
a
,
b
,
c
)
such that
{
a
b
2019
−
c
=
a
b
c
2019
−
a
=
b
c
a
2019
−
b
=
c
\begin{cases}a\sqrt[2019]b-c=a\\b\sqrt[2019]c-a=b\\c\sqrt[2019]a-b=c\end{cases}
⎩
⎨
⎧
a
2019
b
−
c
=
a
b
2019
c
−
a
=
b
c
2019
a
−
b
=
c
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