On the Ternion Cubical Diophantine Equation 5(\(\mathit{m}^2\) + \(\mathit{n}^2\)) -6(\(\mathit{mn}\)) + 8(\(\mathit{m}\)+ \(\mathit{n}\)) + 16 = 370\(\mathit{p}^3\)

Authors

  • P. Saranya PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.
  • G. Janaki PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.
  • K. Poorani PG & Research Department of Mathematics, Cauvery College for Women (Autonomous), Tiruchirappalli – 620 018, Tamil Nadu, India.

DOI:

https://doi.org/10.9734/bpi/mono/978-81-967488-3-8/CH2

Keywords:

Diophantine equation, cubic equation, integer solutions, ternary cubic, narcissistic number

Abstract

The third order Cubic Diophantine equation 5(\(\mathit{m}^2\) + \(\mathit{n}^2\)) -6(\(\mathit{mn}\)) + 8(\(\mathit{m}\)+ \(\mathit{n}\)) + 16 = 370\(\mathit{p}^3\) is analyzed for infinitely enormous number of non-zero integer solutions.  Also, some fascinating relations among the solutions are exhibited.

Published

2023-11-11

How to Cite

P. Saranya, G. Janaki, & K. Poorani. (2023). On the Ternion Cubical Diophantine Equation 5(\(\mathit{m}^2\) + \(\mathit{n}^2\)) -6(\(\mathit{mn}\)) + 8(\(\mathit{m}\)+ \(\mathit{n}\)) + 16 = 370\(\mathit{p}^3\). Explorations in Diophantine Equations, 13–21. https://doi.org/10.9734/bpi/mono/978-81-967488-3-8/CH2

Issue

Explorations in Diophantine Equations

Section

Contents