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Show that a and -a have the same divisors and the same multiples. To show this...

Show that a and -a have the same divisors and the same multiples.

To show this result you must prove the following conditional statements:

  • If d divides a then d divides -a.  
  • If d divides -a then d divides a.
  • If m is a multiple of a then m is a multiple of -a.
  • If m is a multiple of -a then m is a multiple of a.
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