Integer mod proof

  • Thread starter kathrynag
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  • #1
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Homework Statement


Prove that either [tex][a]_{n}[/tex][tex]\cap[/tex][tex]_{n}[/tex]=empty set or [tex][a]_{n}[/tex]=[tex]_{n}[/tex].


Homework Equations





The Attempt at a Solution


I want to assume there is an element x in [tex][a]_{n}[/tex][tex]\cap[/tex][tex]_{n}[/tex] and show this implies [tex][a]_{n}[/tex]=[tex]_{n}[/tex].
This tells me x is in [tex][a]_{n}[/tex] and [tex]_{n}[/tex].
That's where I get stuck.
 
Last edited:

Answers and Replies

  • #2
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sorry, I meant to show this implies [a]=.
 
  • #3
Office_Shredder
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If x=a mod n then n|x-a. x=b mod n means n|x-b.

If x|x-a and n|x-b.... what can you say about a-b?
 
  • #4
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x-a=x-b
x-x=a-b
0=a-b
b=a
 
  • #5
Office_Shredder
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x-a is probably not equal to x-b
 
  • #6
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Ok then I'm not really sure where to go with a-b then.
 

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