quasi
Posts:
12,025
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

