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

2007/08/16 by Alfonso Di Bartolo, Di Bartolo, Alfonso, Giovanni Falcone +1
Mathematics · #11S99 #13K05 #FOS: Mathematics #Number Theory (math.NT) #math.NT #msc:11S99 #msc:13K05

paper · pdf · doi:10.48550/arxiv.0708.2214

7 pages, no figure, submitted

arxiv created 2007/08/16 · arxiv updated 2009/12/01

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.

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