On the p-th root of a p-adic number

Details On the p-th root of a p-adic number On the p-th root of a p-adic number

2007-08-16

arxiv.org/abs/0708.2214v1

Mathematics

Number Theory

7 pages, no figure, submitted

Scientific paper

We give a sufficient and necessary condition for a p-adic integer to have
p-th root in the ring of p-adic integers. The same condition holds clearly for
residues modulo p^k. We give a proof that Fermat's last theorem is false for
p-adic integers and for residues mod p^k.

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