# An algebra problem by Ankit vijay

Algebra Level 5

For an integer $$n$$, let $$f_9(n)$$ denote the number of positive integers $$d\leq 9$$ that divide $$n$$. Suppose that m is a positive integer and $$b_1,b_2,\ldots,b_m$$ are real numbers such that $$f_9(n)=\textstyle\sum_{j=1}^mb_jf_9(n-j)$$ for all $$n>m$$. Find the smallest possible value of $$m$$

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