Solutions to x^3 + y^3 + z^3 = 6xyz/Mistake
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Source Work
1997: David Wells: Curious and Interesting Numbers (2nd ed.):
- The Dictionary
- $6$
Mistake
- The equation $x^3 + y^3 + z^3 = 6 x y z$ has the unique solution $x = 1$, $y = 2$, $z = 3$.
Correction
The correct answer is as given in Solutions to $x^3 + y^3 + z^3 = 6 x y z$
The Diophantine equation:
- $x^3 + y^3 + z^3 = 6 x y z$
has exactly two kinds of solutions in the integers:
\(\ds \set {x, y, z}\) | \(=\) | \(\ds \set {n, 2 n, 3 n}\) | for some $n \in \Z$ | |||||||||||
\(\ds \set {x, y, z}\) | \(=\) | \(\ds \set {0, n, -n}\) | for some $n \in \Z$ |
Sources
- 1997: David Wells: Curious and Interesting Numbers (2nd ed.) ... (previous) ... (next): $6$