Indulul's function

Algebra Level 4

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

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

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

This problem is posed by Indulal G.

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