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If a divides b and b divides a then either a is equal to b or a is equal to -b.

Additional note:

if a divides b, there exist a p such that ap=b.

and if b divides a, there exist a q such that a=bq.

then ap=(bq)p=b

=> b(1-pq)=0

=> pq=1 since b!=0

=> p=q=1 or p=q=-1

=> a=b or a=-b

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