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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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