Simultaneous Diophantine Equations for Powers 1, 2, 4 and 6

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Let and be arbitrary complex numbers.

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Set

,

,

,

,

and

,

,

,

.

Then for ,

.

If and are integers, we get simultaneous Diophantine equations; for example:

,

,

,

.

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Contributed by: Minh Trinh Xuan (August 2022)
Open content licensed under CC BY-NC-SA


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