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Given that $\displaystyle{a+b\sqrt[3]{2} +c\sqrt[3]{4} =0}$, where $a,b,c$ are integers. Show $a=b=c=0$

Do I use modular arithmetic?

  • 4
    Do you know what a basis of a field extension is? Can you think of a field extension (with a known basis) that would be useful in your problem? Modular arithmetic won't help you here.2012-03-15
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    I am not sure, but it was a problem from AwesomeMath last year2012-03-15
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    I'm not familiar with AwesomeMath. What tools/theory do they think the solvers should be familiar with?2012-03-15
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    Try using the converse.2012-03-15
  • 0
    See https://math.stackexchange.com/questions/158722/2018-11-25

3 Answers 3