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 Nov 22 accepted Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ Nov 20 comment Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ Ok , so if im going on that way , the list of the generators and i can get from discovering that 3 is a generator and use gcd (m,p-1) is 3,10,5,11,14,7,12,6 that 8 generators , so i need to fine 1 more generators and from him to get another list of generators? and like that to find at least 12 generators? Nov 20 comment Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ 2 is not a generator of $\Bbb Z^*_17$. 2^1=2 2^2=4 2^3=8 2^4=16 2^5=15 2^6=13 2^7=9 2^8=1. and $\Bbb Z^*_17$ ={1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16} Nov 20 comment Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ Tobias - i read it again and i got it , its true. but how do i show that the set of all elements that are NOT-GENERATORS are a sub-group ? Nov 20 comment Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ the exersize have 2 section , the first one is the one i solved and describe above . im looking for a hint for the second one for the non-generators Nov 20 comment Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ some thing dose not add up for me , lets take p=17 p-1=16 3 is a generator of this group , m=16 gcd(16,16)=16 Nov 20 comment Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ can you explain a bit more your answer ? Nov 20 asked Trying to prove that a set of non-generators element are not a subgroup of $\Bbb Z^*_p$ Nov 17 awarded Scholar Nov 17 accepted Trying to prove that a $\Bbb Z^*_n$ group is not cyclic Nov 17 comment Trying to prove that a $\Bbb Z^*_n$ group is not cyclic is there any fast way to calculate it ? we just started the course , im not sure i have the tools to answer that. Nov 17 comment Trying to prove that a $\Bbb Z^*_n$ group is not cyclic i mean for a multiplicative group Zn Nov 17 asked Trying to prove that a $\Bbb Z^*_n$ group is not cyclic