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Minimum distance between sets (
Posted on 2023-08-21
)
Let m,n be positive integers greater than 1. We define the sets P
m
={1/m, 2/m, ..., (m-1)/m} and P
n
={1/n, 2/n, ..., (n-1)/n}.
Find the distance between P
m
and P
n
, that is defined as min{|a-b|: a∈P
m
, b∈P
n
}
No Solution Yet
Submitted by
Danish Ahmed Khan
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answer (spoiler)
Comment 1 of 1
This seems like a D1. Am I missing something?
If m and n have a common factor, the distance is zero.
Otherwise the distance is 1 / (m * n).
Posted by
Charlie
on 2023-08-21 08:56:10
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