Track / Stage 5 / 147 of 400 #747 of 1964

Problem 747

AIME late

Number theory Difficulty 5.4 Prove it

20. How many 89-complete partitions have the smallest number of parts? What are their part numbers?

将上面的文本翻译成英文，请保留源文本的换行和格式，直接输出翻译结果。

This one wants a proof. Work it on paper, then read the official solution and mark yourself. Be honest about it: the record is only any use to you if it is.

Official solution

20. 12,9

Source: NuminaMath-1.5, licensed Apache-2.0. Statement and solution reproduced as published; topic, difficulty and ordering added by this site.