I would really just like a hint or a nudge in the right direction. I feel pretty comfortable with irreducibility over a single variable, but I haven't been exposed to many multivariable questions.
Thanks for the help.
2026-03-30 05:13:16.1774847596
Is $X^5+Y^5-1$ irreducible in $\mathbb{C}[X,Y]$?
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Yes: see it as $f(X)\in (\Bbb C[Y])[X]$ and apply Eisenstein with the prime $Y-1$.