4
votes
$a^3 + b^3 + c^3 = 4abc$ has no positive integer solutions
well, why not. You mention factoring. As you say, $x^3 + y^3 + z^3 - 3xyz$ factors over the rationals and factors completely over the complexes, by adding in cube roots of $1.$ However, your ...
- 141k
3
votes
Accepted
Weierstrass Form of degree 4 equation
Yes this is an elliptic curve, and yes we can put it in Weierstrass form. An unhelpful simple answer is that computer algebra will achieve this for you (...
- 4,152
1
vote
$a^3 + b^3 + c^3 = 4abc$ has no positive integer solutions
I may have an approach, but not the finished solution, for this... Without loss of generality, we may order the positive integers
$$a \ge b \ge c$$
Now there exist integers $d, e \ge 0$ such that
$$ a^...
- 812
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