If $a,b,c$ are integers such that $4a^3+2b^3+c^3=6abc$ , then is it true that $a=b=c=0$ ? I was thinking of infinite descent but can’t actually proceed , please help. Thanks in advance

just so this doesn’t get deleted, I want to make it clear that I already know how to solve this using the UFD $\mathbb{Z}[\sqrt{-2}]$, and am in search for the infinite descent proof that Fermat claimed to have found. I’ve alaways been fascinated by this Diophantine equation $x^2+2=y^3$ in particular ever since I saw it, […]

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