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I want to find a '$c$' such that $c$ $\in \mathbb{Q}$ and $x^3+y^3+z^3=c$ has no solutions over rationals.

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  • 1
    $\begingroup$ What about $\pi$? $\endgroup$
    – baharampuri
    Oct 6, 2015 at 17:04
  • 4
    $\begingroup$ @baharampuri It is not a Rational number $\endgroup$
    – xyz
    Oct 6, 2015 at 17:06
  • $\begingroup$ Oh i see, $c \in \mathbb{Q}$. $\endgroup$
    – baharampuri
    Oct 6, 2015 at 17:07
  • 7
    $\begingroup$ There is no such $c\in\Bbb Q$, see here journals.cambridge.org/… $\endgroup$
    – Wojowu
    Oct 6, 2015 at 17:08
  • 3
    $\begingroup$ Does $c=0$ work for you? The only solutions of $x^3+y^3+z^3=0$ are the trivial ones. This equivalent to the Fermat equation $x^3+y^3=(-z)^3$. $\endgroup$
    – lhf
    Oct 6, 2015 at 17:53

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