Perfect powers in sum of three fifth powers

نویسندگان

چکیده

In this paper we determine the perfect powers that are sums of three fifth in an arithmetic progression. More precisely, completely solve Diophantine equation(x−d)5+x5+(x+d)5=zn,n≥2, where d,x,z∈Z and d=2a5b with a,b≥0.

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ژورنال

عنوان ژورنال: Journal of Number Theory

سال: 2022

ISSN: ['0022-314X', '1096-1658']

DOI: https://doi.org/10.1016/j.jnt.2021.07.029