Floor function

Algebra Level 5

\[ x - f(x) = 19 \left \lfloor \frac x{19} \right \rfloor - 90 \left \lfloor \frac {f(x)}{90} \right \rfloor \\ 1900 < f(1990) < 2000 \]

Suppose \(f: N \rightarrow N \) satisfies the conditions above, find the sum of all possible values of \(f(1990)\).

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