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2021-02-01 04:55:10 +0100 commented question integer solutions to this system of equations

No just trying to solve!

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2021-01-31 15:19:04 +0100 asked a question integer solutions to this system of equations

Consider the following system of two equations: $$ x + y + z = 24 n + 3 $$ $$ x y z = 576 n³ + 216 n^2 + 27 n - 25 $$

For what value of $n$ are there integer solutions $x$, $y$, $z$?

Can someone help me to write down a code for the above!