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Sep 22, 2021 at 15:15 comment added user142929 While my conjectures are both false, your examples of families of solutions provide more value to the equations/problems $(1)$ and $(2)$.
Sep 22, 2021 at 15:09 comment added user142929 Many thanks, what good counterexamples! I'm accepting your answer. Feel free to study the (veracity of conjectures) case $n$ odd for these equations, if it is interesting for your work.
Sep 22, 2021 at 15:09 vote accept user142929
Sep 20, 2021 at 19:45 history edited Max Alekseyev CC BY-SA 4.0
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Sep 20, 2021 at 19:34 history edited Max Alekseyev CC BY-SA 4.0
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Sep 20, 2021 at 19:22 history answered Max Alekseyev CC BY-SA 4.0