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Topic: floor sums
Replies: 21   Last Post: Oct 18, 2013 2:39 PM

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quasi

Posts: 10,403
Registered: 7/15/05
floor sums
Posted: Oct 13, 2013 5:51 AM
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Let [x] denote floor(x).

Prove or disprove:

If a,b,c,d are positive integers such that

a < b < c < d

a + d = b + c

and f: R -> Z is defined by

f(x) = [ax] + [dx] - [bx] - [cx]

then

min({f(x) | x in R}) = -1

max({f(x) | x in R}) = 1

Remark:

I don't have a lot of confidence in the above claim but the
data appears to support it.

quasi



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