I wish to show if for sufficiently large integers N, and a given prime p, the polynomial $x(x − N p^2)(x + N p^2)(x^2 + N^2p^4) + p $ can be solved by radicals. I think the answer is no but I am not sure how to prove~
2026-03-26 22:57:56.1774565876
$x(x − N p^2)(x + N p^2)(x^2 + N^2p^4) + p $ cannot be solved by radicals
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