English

On the Diophantine equation $B_{n_{1}}+B_{n_{2}}=2^{a_{1}}+2^{a_{2}}+2^{a_{3}}$

Number Theory 2023-06-22 v2

Abstract

In this study we find all solutions of the Diophantine equation Bn1+Bn2=2a1+2a2+2a3B_{n_{1}}+B_{n_{2}}=2^{a_{1}}+2^{a_{2}}+2^{a_{3}} in positive integer variables (n1,n2,a1,a2,a3),(n_{1},n_{2},a_{1},a_{2},a_{3}), where BnB_{n} denotes the nn-th balancing number.

Keywords

Cite

@article{arxiv.2212.06372,
  title  = {On the Diophantine equation $B_{n_{1}}+B_{n_{2}}=2^{a_{1}}+2^{a_{2}}+2^{a_{3}}$},
  author = {Kisan Bhoi and Prasanta Kumar Ray},
  journal= {arXiv preprint arXiv:2212.06372},
  year   = {2023}
}

Comments

18 pages