Diophantine Equations with Powers of Two or Four for Thirteen Variable Sets

Let , , be three arbitrary complex numbers.
Set
,
,
,
,
,
,
,
,
,
,
,
,
and
,
,
,
,
,
,
,
,
,
,
,
,
.
Then for ,
.
If , , are integers, we get a Diophantine equation.
For example,

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