
Special M (Solved)
Let denote the golden ratio,
and let
denote the floor function. For fixed
, let
, let
, and let
. We can expect
to have about the same growth rate as
.
Conjecture Prove or disprove that for every fixed
, as
ranges through all the positive integers, there is a number
such that
takes each of the values
infinitely many times, and
. (Can you formulate
as a function of
? Generalize for other numbers
?)









Bibliography
http://faculty.evansville.edu/ck6/integer/unsolved.html
* indicates original appearance(s) of problem.