Observations On Ternary Quadratic Diophantine Equation

The Ternary Quadratic Diophantine Equation is given by 2 2 2 8(x  y ) 15xy  7x  7 y  49  40z . Number of non-zero distinct integer solutions. Some interesting relations among the solutions and the way of factorization, along with the illusion of non-zero distinct integer solutions to the above equations are obtained.