English

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

Number Theory 2007-08-17 v1

Abstract

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.

Keywords

Cite

@article{arxiv.0708.2214,
  title  = {On the p-th root of a p-adic number},
  author = {Alfonso Di Bartolo and Giovanni Falcone},
  journal= {arXiv preprint arXiv:0708.2214},
  year   = {2007}
}

Comments

7 pages, no figure, submitted

R2 v1 2026-06-21T09:08:00.158Z