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8.5
{a, b,c,a^2/b, b^2/c, c^2/a} - All-Russian MO 2004 Regional (R4) 8.5
{a, b,c,a^2/b, b^2/c, c^2/a} - All-Russian MO 2004 Regional (R4) 8.5
Source:
September 27, 2024
number theory
Problem Statement
Can a set of six numbers
{
a
,
b
,
c
,
a
2
b
,
b
2
c
,
c
2
a
}
\left\{a, b,c, \frac{a^2}{b} , \frac{b^2}{c} , \frac{c^2}{a} \right\}
{
a
,
b
,
c
,
b
a
2
,
c
b
2
,
a
c
2
}
, where
a
,
b
,
c
a, b, c
a
,
b
,
c
positive numbers, turn out to be exactly exactly three different numbers?
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