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Jul 20, 2018 at 0:06 comment added Anton Klyachko Indeed, we were unaware of Euler's result.
Jun 22, 2018 at 2:31 comment added Zhi-Wei Sun For any rational number $x$, by Euler's result we can write $-x$ as $abc(a+b+c)$ with $a,b,c\in\mathbb Q$, thus $x=abcd$ with $d=-a-b-c$, and $a+b+c+d=0$. So Euler's result for $k=3$ essentially implies that $k\ge5$ is good.
Jun 16, 2018 at 17:56 vote accept Dominic van der Zypen
Jun 16, 2018 at 17:55 vote accept Dominic van der Zypen
Jun 16, 2018 at 17:56
Jun 16, 2018 at 17:19 history edited Jeremy Rouse CC BY-SA 4.0
Fixed a typo in the last equation.
Jun 16, 2018 at 16:47 history answered Jeremy Rouse CC BY-SA 4.0