so I have to prove that a^3-2b^3-4c^3 = 0 has no positive integer solutions. I have gotten through most of the proof but now I am stuck, and if you guys could give me a nudge in the right direction that would be great.(adsbygoogle = window.adsbygoogle || []).push({});

work done so far:

proof by contradiction, i assumed that a^3-2b^3-4c^3 = 0 does have a positive int solution, therefore by the well ordering principle it has a least solution a = a* , b = b*, c = c*. I then proceeded to show that a*^3 = 2b*^3+4c*^3, therefore a*^3 is an even number, and so a* is also even. I let a* = 2k and plugged that back into the equation to get the following: 8(k^3) = 2b*^3+4c*^3. Now i am stuck. If you guys could give me a nudge in the right direction that would be great, I know that i want to show that k is also a solution to the original equation therefore contradicting that a* is the least solution, thanks for the help.

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# Homework Help: Proving that a^2-2b^2-4c^2 = 0 has no positive integer solutions

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