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December 2

Number of Factorizations

Hi, I know that $\mathbb {Z} _{n}$ (ring of integers modulo n) is not a Unique Factorization Domain (for non-prime n), so there're numbers with non-unique factorization. So, my question is: how many factorizations modulo n exist for a number m? עברית (talk) 07:56, 2 December 2016 (UTC)[reply]

Perhaps I'm being dim, but do you have an example showing that Z_n isn't a UFD? --RDBury (talk) 00:27, 3 December 2016 (UTC)[reply]

They mean for instance 1=1x1=2x3=4x4 (mod 5). I don't know what the mean by factorizations though - one could have any number of factors like for instance 2x2x2x2 or 4x3x3. Dmcq (talk) 00:44, 3 December 2016 (UTC)[reply]

Z_n is not a domain (except if n is prime), so it can't be a UFD. That doesn't mean it doesn't have the unique factorization property though. But I just thought of an example: 6=2⋅3=2⋅3⋅3=2⋅3⋅3⋅3=2⋅3⋅3⋅3⋅3... (mod 12) so the number of factorizations is infinite. --RDBury (talk) 01:09, 3 December 2016 (UTC)[reply]

@Dmcq: Z₅ is a field, so all values (except 0) are units, and there are no primes. None of your examples really count as distinct "factorizations" in this context; factors of units are ignored. --Trovatore (talk) 01:22, 3 December 2016 (UTC)[reply]

Thanks. I was trying to figure out what they meant. Dmcq (talk) 11:46, 3 December 2016 (UTC)[reply]

Website that helps you make math questions

Is there a website that helps you make a math question like for example I want to make a math question about set theory. In this question, I want to make three circles Venn diagram connecting together and each circle has a number like 23 people like comedy genre movies only, 24 people like action genre movies only, 19 like horror genre movies only, 5 people like comedy and action movies but not horror, 6 people like action and horror movies but not comedy, and 10 people like comedy and horror movies but not action and in the middle of the diagram, 10 people like all three movie genres. Then, I make questions like what is A ∩ C ∩ H, A ∩ C ∪ H, and etc? Donmust90 (talk) 15:24, 2 December 2016 (UTC)Donmust90Donmust90 (talk) 15:24, 2 December 2016 (UTC)[reply]

I would approach this by Googling for blank Venn diagrams with the appropriate number of circles, then edit them to add the elements you want. You might consider just putting single letters and maybe digits in the diagram, allowing 26 or 36 elements (you can add Greek letters, etc., if you need more), and then use an index to map each to the full description. Otherwise, the Venn diagrams can get very crowded quickly. MS Paint allows you to add text to an existing pic, as do any number of software packages. StuRat (talk) 15:39, 2 December 2016 (UTC)[reply]

I use Ordinal Fractions in those situations.

100 C: comedy
200 no comedy
010 A: action
020 no action
001 H: horror
002 no horror
122 23
212 24
221 19
112 5 
211 6
121 10
111 A ∩ C ∩ H: 10

See [1]. Bo Jacoby (talk) 15:37, 5 December 2016 (UTC).[reply]