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Solutions to $a (2 a^2 + 2 b^2 + c^2 + d^2) = (2 a^3 + 2 b^3 + c^3 + d^3)$ in integers

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-1 1 I ask for positive integral solutions to $a (2 a^2 + 2 b^2 + c^2 + d^2) = (2 a^3 + 2 b^3 + c^3 + d^3)$ , where a,b,c,d are positive integers and $aneq bneq cneq d$ . In particular does a solution exist for $d>1$ . number-theory share | cite | improve this question asked 2 days ago user631773 user631773 1 1 New contributor user631773 is a new contributor to this site. Take care in asking for clarification, commenting, and answering. Check out our Code of Conduct.