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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