I know that the generating function for the number of integer partitions of $n$ into distinct parts is $$\sum_{n \ge 0} p_d(n)x^n = \prod_{i \ge 1}(1+x^i)$$ I'm trying to use this generating function to show that the number of integer partitions of $n$ into parts not divisible by $d$ equals the number of integer partitions of $n$ in which no part appears more than $d-1$ times. I'm not sure how to proceed.
2026-04-02 02:45:17.1775097917
Question about number of generating functions
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