20200710, 04:26  #1 
May 2004
2^{2}·79 Posts 
A tentative question
There seems to be no nonresidues higher than quadratic order;is this related to Fermat's last theorem?
Last fiddled with by devarajkandadai on 20200710 at 04:37 
20200710, 13:01  #2 
"Alexander"
Nov 2008
The Alamo City
3^{2}·7^{2} Posts 
If I'm understanding you right, you're saying there are no, say, cubic nonresidues. Well 4 is a cubic nonresidue modulo 7 (there is no x where x^3=4 (mod 7)).

20200710, 14:02  #3  
Nov 2003
2^{2}·5·373 Posts 
Quote:
If p = 1 mod 6, how many cubic residues does it have? how many nonresidues? What about p = 1 mod 6? Did you bother at all to even try to answer your own question? Do us all a favor. Don't come back until you take the time to actually do some reading about this subject. And if you can't be bothered, then don't come back at all. Your question could have been answered with 15 seconds of thought. But of course you could not be bothered. 

20200710, 14:07  #4  
Undefined
"The unspeakable one"
Jun 2006
My evil lair
1773_{16} Posts 
Quote:


20200710, 15:13  #5 
Nov 2003
1D24_{16} Posts 

20200710, 16:34  #6  
Bamboozled!
"πΊππ·π·π"
May 2003
Down not across
2^{2}×37×71 Posts 
Quote:
You clicked on the "Quote" button, not the "Post Reply" button. Technical point in that your text clearly addressed the OP, not the person you quoted in the technical sense. Last fiddled with by xilman on 20200710 at 16:34 

20200710, 22:38  #7  
Nov 2003
2^{2}×5×373 Posts 
Quote:
What I wrote was a followon. It was suggested by Happy5214 that the O.P. check whether 4 mod 7 was a cubic residue. I simply extended this to other primes that were: firstly 1 Mod 6 (as 7 is) and then to all other primes. [And added some admonishment.] From now on I will try to use the "post reply" button instead of "quote" to avoid confusion when I do not intend to quote anything. Last fiddled with by R.D. Silverman on 20200710 at 22:45 Reason: some word changes 

20200710, 22:45  #8 
Undefined
"The unspeakable one"
Jun 2006
My evil lair
3^{2}×23×29 Posts 

20200710, 23:58  #9  
Mar 2019
8F_{16} Posts 
Quote:
Why is this sort of rude, insulting tone permitted on the forums? Certainly this vitriol and condescension discourages people from asking questions and thereby learning. Even if the answers may be trivially obvious to Mr. Silverman, they are not to others. 

20200711, 00:51  #10  
Nov 2003
2^{2}×5×373 Posts 
Quote:
a proven unwillingness to spend time learning anything about the subject. He also fails to respond to questions posed to him. Anyone who wants to ask questions needs to show that they have made at least a minimal effort to answer the question for themselves. To do so otherwise is rude in and of itself because it places a time requirement on others. Even a cursory web search by the O.P. would have revealed the answer. Teachers should not have to waste their time with students who are unwilling to do basic homework. 

20200711, 00:52  #11  
"Serge"
Mar 2008
Phi(4,2^7658614+1)/2
22056_{8} Posts 
Eh... There is a button for that.
Quote:
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