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If two monic polynomials of $\mathbb{Z}_p[X]$ (p-adic integer coefficient) are relatively prime modulo p, then do they generate $\mathbb{Z}_p[X]$?
I'm currently reading a paper of Rene Schoof, and I got stuck in a line. And I'm trying to check the above sentence.
Although that seems to be elementary, I hope someone can give me a counterexample ...
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