Indulul's function

Algebra Level 4

Let \(f(x)\) be a function satisfying \(f(1) =101\) and

\[\begin{align} f(x+5) & \geq f(x)+5\\ f(x+1) & \leq f(x)+1, \end{align} \]

for all positive integers \(x \). What are the last three digits of \(f(2013)?\)

This problem is posed by Indulal G.

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