An ordered R-module M with a distinguished element 1 > 0 is called integrally divisible if for each scalar 0 < r in R, any m from M can be divided by r with a remainder (i.e. m = rn + i for some n, i from M with 0 <= i < r1). I show that all definable sets in such a module M are "protoperiodic" and therefore M satisfies quantifier elimination up to bounded formulas. This result is particularly interesting if understood in a wider context of model theory of linear arithmetics. I will try to give a brief survey of this arithmetical background.