Proof on the divisibility of integers

AI Thread Summary
To prove that if integer a divides integer b and b divides a, then a must equal b or a must equal -b, start by expressing b as aj and a as bk, where j and k are integers. Substituting these expressions into each other leads to the equations a = ajk and b = bkj. Analyzing these relationships reveals that the only integer solutions occur when either a equals b or a equals -b. This conclusion is supported by the properties of divisibility and integer multiplication. The proof ultimately confirms the stated divisibility condition.
kolley
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Homework Statement



Let a,b be integers where a doesn't =0. Prove that if a divides b, and b divides a, then a=b or a=-b

The Attempt at a Solution



I started out with b=aj and a=bk, where j,k are integers. Don't quite know how to proceed
 
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Substitute the expression for a or b into the other equation. What do you get?
 

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