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