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December 30th, 2013, 05:16 AM  #11  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Re: Cube roots of 1 Quote:
 
December 30th, 2013, 05:28 AM  #12  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Cube roots of 1 Quote:
But, for the sake of keeping everything fair, I'd rather not but simply say that yes, mine indeed is not representable in a single term (or apparently so). But if simplified, you get which is less "uglier" than that of the one you presented.  
December 30th, 2013, 05:43 AM  #13 
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Re: Cube roots of 1
Terms are separated by addition and/or subtraction, so, for instance, has 3 terms as written, and is a single term as written. So how would you represent 3 in terms of your beautiful method using ? 
December 30th, 2013, 05:44 AM  #14  
Math Team Joined: Apr 2010 Posts: 2,780 Thanks: 361  Re: Cube roots of 1 Quote:
Could this be what you're looking for:  
December 30th, 2013, 05:52 AM  #15  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Cube roots of 1 Quote:
As for representing 3, perhaps square it? PS : My representation is nothing of much "beauty" although it is of interest, yes. Have you searched the keywords I have italicized?  
December 30th, 2013, 05:54 AM  #16  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Cube roots of 1 Quote:
 
December 30th, 2013, 05:56 AM  #17  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Re: Cube roots of 1 Quote:
 
December 30th, 2013, 06:12 AM  #18  
Math Team Joined: Jul 2011 From: North America, 42nd parallel Posts: 3,372 Thanks: 234  Re: Cube roots of 1 Quote:
All i have to do is put a factor of 2 in front of the using my single term result for Quote:
 
December 30th, 2013, 06:16 AM  #19  
Math Team Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory  Re: Cube roots of 1 Quote:
 

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