Dilated Floor Functions That Commute

Jeffrey C. Lagarias, Takumi Murayama, D. Harry Richman
2016 The American mathematical monthly  
We determine all pairs of real numbers (α, β) such that the dilated floor functions α x and β x commute under composition, i.e., such that αβ x = βα x holds for all real x.
doi:10.4169/amer.math.monthly.123.10.1033 fatcat:tubwi33vrrf2fd7keqb2bndhd4