On Integer Solutions of the Ternary Bi-Quadratic Diophantine Equation 14 (x²+y²) -24xy=17z⁴

Key Points

• The investigation identifies integral solutions to the diophantine equation through various patterns.
• Up to four distinct solution patterns are explored to understand the relationships between the solutions.
• Assessment of unique polygonal numbers contributes to the understanding of the equation's properties and integrality issues.  The findings suggest deeper connections among distinct solutions, defining a framework for future studies in number theory.