Proof on the divisibility of integers

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SUMMARY

The discussion centers on proving that for integers a and b, if a divides b and b divides a, then it must follow that a equals b or a equals negative b. The initial approach involves expressing b as aj and a as bk, where j and k are integers. The next logical step is to substitute one expression into the other to derive a conclusive proof.

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  • Understanding of integer divisibility
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  • Knowledge of mathematical proofs
  • Basic concepts of number theory
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  • Explore formal proof techniques in mathematics
  • Review examples of divisibility proofs
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Students studying number theory, mathematics enthusiasts, and anyone interested in formal proof techniques related to integer properties.

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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