Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

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

 Messages: [ Previous | Next ]
 quasi Posts: 11,916 Registered: 7/15/05
floor sums
Posted: Oct 13, 2013 5:51 AM

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

Date Subject Author
10/13/13 quasi
10/13/13 scattered
10/13/13 scattered
10/13/13 Leon Aigret
10/13/13 Richard Tobin
10/13/13 James Waldby
10/13/13 quasi
10/13/13 quasi
10/14/13 quasi
10/14/13 gnasher729
10/15/13 quasi
10/15/13 quasi
10/16/13 quasi
10/16/13 quasi
10/18/13 quasi
10/18/13 quasi
10/18/13 quasi
10/18/13 quasi
10/14/13 Don Redmond
10/14/13 quasi
10/15/13 quasi
10/15/13 Don Redmond