# Functions struggling with the modulo

Let $$f$$ be a cubic polynomial function with integer coefficients and $$a \equiv b \text{ (mod 9)}$$, where $$a$$ and $$b$$ be natural numbers.

Then, if you divide the expression $$|f(a)-f(b)|$$ by 18, what would be the nature of the decimal expansion (after radix point) of the resulting expression?

Explanation: For example, the decimal expansion after the radix point of 299.12123123412345... is 12123123412345....

Bonus: Try to find out the repeating digits in the expansion, if it is non-terminating.

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