Representing Even Perfect and Near-Perfect Numbers as Sums of Cubes

Authors

  • Padma Bhushan Borah
  • Pankaj Jyoti Mahanta
  • Manjil Saikia

Abstract

Motivated by recent results of Farhi and Ulas we show that for each $n\equiv \pm 1 \pmod 6$, the Diophantine equation $2^{n-1}(2^n-1)=x^3+y^3+z^3$ has at least three solutions. We also prove results about the representation of even near-perfect numbers with two distinct prime factors as sums of integral cubes.

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Published

22-09-2022

How to Cite

Borah, P. B., Mahanta, P. J., & Saikia, M. (2022). Representing Even Perfect and Near-Perfect Numbers as Sums of Cubes. Journal of the Assam Academy of Mathematics, 12, 1–7. Retrieved from https://jaam.aamonline.org.in/ojs/index.php/j/article/view/57

Issue

Section

Original Research Articles