# 2015 Countdown Problem #15: Palindrome Integration

Algebra Level 5

Let $$x$$ be a real number and $$f(x)$$ be a real-valued function on $$x$$ such that $$f(x)$$ is:

• the next palindrome larger than $$x$$ (if $$x$$ is not a palindrome); or

• $$x$$ (if $$x$$ is a palindrome).

For example, $$f(1001)=1001$$,$$f(1001.01)=f(1002)=1111$$.

Let

$A=\int _{ 999 }^{ 2015 }{ f(x) \mbox{ } dx }$

$B=f(...(f(f(1603)-58)-58)...)-58$

Find the value of $$\frac{A}{B}$$.

This problem is part of the set 2015 Countdown Problems.

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