Proof on the divisibility of integers

Thread starter kolley
Start date Feb 16, 2010
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Divisibility Integers Proof

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.

Feb 16, 2010

kolley

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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Feb 16, 2010

Mark44

Mentor

Insights Author

Substitute the expression for a or b into the other equation. What do you get?

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