Let f be a function defined on the set of non-negative integers and taking values in the same
set. Given that
(a) \displaystyle x \minus{} f(x) \equal{} 19\left[\frac{x}{19}\right] \minus{} 90\left[\frac{f(x)}{90}\right] for all non-negative integers x;
(b) 1900<f(1990)<2000,
find the possible values that f(1990) can take.
(Notation : here [z] refers to largest integer that is ≤z, e.g. [3.1415] \equal{} 3). functionalgebra proposedalgebra