Integral solutions of certain Diophantine equation in quadratic fields

2022/05/29 by Sharma, Richa
#11D25 #11D41 #11G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2205.14689

Abstract

Let K= Q(√(d)) be a quadratic field and O_K be its ring of integers. We study the solvability of the Diophantine equation r + s + t = rst = 2 in O_K. We prove that except for d= -7, -1, 17 and 101 this system is not solvable in the ring of integers of other quadratic fields.

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