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x+y+z=24n+3 xyz=576n³+216n²+27n-25

For what value of n, x,y,z are integers? Can someone help me to write down a code for the above!

x+y+z=24n+3 xyz=576n³+216n²+27n-25Consider the following system of two equations: $$x + y + z = 24 n + 3$$ $$x y z = 576 n^2 + 216 n^2 + 27 n - 25$$

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

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

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

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

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