Question Number 215898 by F_Physics last updated on 21/Jan/25

$${x}^{{n}} +{y}^{{n}} +{z}^{{n}} \:=\:\mathrm{0} \\ $$$${n}\:=\:? \\ $$
Commented by Rasheed.Sindhi last updated on 21/Jan/25

$${For}\:{x}={y}={z}=\mathrm{0},\:{n}\in\mathbb{R}^{+} \\ $$
Answered by Eze120 last updated on 23/Jan/25

$${n}\in\mathbb{R} \\ $$$${If}\:{x},{y}\:{and}\:{z}\:{the}\:{same}\:{than}\:\mathrm{0} \\ $$$${PD}:−{n}\:{is}\:{indefinided}. \\ $$