Time: 9:30 - 11:30, March 17, 2021
Venue: Room 612, A6, Institute of Mathematics, VAST

Abstract: In this talk, we give some applications of p-adic numbers to Diophantine equations. In particular, we present a technique to prove the nonexistence of positive rational points on some curves and surfaces. One of our earlier results in this direction is to show that equation (x+y+z+w)(1/x+1/y+1/z+1/w)=n does not have solutions in positive integers if n=4m^2 or n=4m^2+4, where 4 does not divide m-2. Our current work is to show that equation x/y+y/z+z/x+x/w=n does not have solutions in positive integers if 8|n or n=4q, where q^2-1=p.2^h, 2|h, h>3, and 8|p+1. This is joint work with Erik Dof.