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National and Regional Contests
Russia Contests
Saint Petersburg Mathematical Olympiad
2022 Saint Petersburg Mathematical Olympiad
6
6
Part of
2022 Saint Petersburg Mathematical Olympiad
Problems
(1)
Representation as ratio if two fractional parts
Source: St Petersburg 2022 11.6
9/28/2022
Find all pairs of nonzero rational numbers
x
,
y
x, y
x
,
y
, such that every positive rational number can be written as
{
r
x
}
{
r
y
}
\frac{\{rx\}} {\{ry\}}
{
ry
}
{
r
x
}
for some positive rational
r
r
r
.
algebra