The question given was to find an example of ring with prime characteristics such that its two different roots of $f=X^p-a$ both have multiplicity p. I can only think of $\mathbb{Z}/p\mathbb{Z}$. The main takeaway for this problem is to show that for some cases of the ring with prime characteristics, sum of multiplicities of roots can exceed the degree of f.
2026-05-15 23:50:03.1778889003
Easy example for commutative ring with prime characteristics that has two different roots for $f=x^p-a$?
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