Is there a method to find the minimum number of generators ##\big<a_1,a_2,\cdots,a_k\big>## needed to generate ##\mathbb{Z}_n^*## such that ##\mathop{\cap}\limits_{n=1}^k \big<a_n\big>=\{1\}## other than by just looking for them and checking orders and products of group elements?(adsbygoogle = window.adsbygoogle || []).push({});

For example, what would be the minimum generator set for ##\mathbb{Z}_{100!}^*##?

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# Find minimum number of generators for Z/nZ

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