Non-Trivial Integral Solutions of Ternary Quadratic Diophantine Equation

Abstract

The ternary quadratic equation ?^(2 )+?^2-14?+10?=74(?^2-1) representing cone is analyzed by its nonzero distinct integer points on it. Employing the integer solutions, a few relations between the solutions and some patterns are presented.

Introduction

Conclusion

In this paper, we have made an attempt to obtain infinitely many non-zero distinct integer solutions to the equation given by ?^(2 )+?^2-14?+10?=74(?^2-1) . As ternary quadratic equations are rich in variety, one may search for the other choice of ternary quadratic Diophantine equations and determine their integer solutions along with suitable properties.

References

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Copyright

Copyright © 2024 Manju Somanath, Vinmol K Jesudas. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.