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Separation of distinct reduced fractions
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Mathematics
Area of mathematics
Number theory
Diophantine approximation
Liouville approximation theorem
Created
2026-09-24
Updated
2026-09-24
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For distinct
reduced fractions
p
/
q
and
u
/
v
,
q
p
−
v
u
=
q
v
∣
p
v
−
q
u
∣
≥
q
v
1
.
(1)
If
q
>
v
, this is strictly greater than
q
−
2
.
Ancestors
(6)
Liouville approximation theorem
Diophantine approximation
Number theory
Area of mathematics
Mathematics
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Past exam of the mathematics course of the University of Cambridge
/
2023
/
ii
/
Paper 1
/
2F
/
b
/
Solution
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