I want to find the solutions in R of , where ⌊x⌋ is the unique integer such that .
I solved it as follows. Let . By the definition, . Then , , , and finally, . (1).
Now I analyzise n modulo 3.
If , then (1) becomes . Then either , or . From the equation itself, it follows that , or , so or . It's easy to turn this into 2 intervals for x.
Similarly, I can continue for and . This seems to lead to a solution, but is there perhaps a better way? Thank you for any ideas/verification of my solution.