Frobenius Numbers Associated with Diophantine Triples of x²-y²=z^r

We give an explicit formula for the p-Frobenius number of triples associated with Diophantine Equations $x^2-y^2=z^r$ ($r\ge 2$), that is, the largest positive integer that can only be represented in p ways by combining the three integers of the solutions of Diophantine equations $x^2-y^2=z^r$. This result is also a generalization because if $r=2$ and $p=0$, the (0-)Frobenius number of the Pythagorean triple has already been given. To find p-Frobenius numbers, we use geometrically easy to understand figures of the elements of the p-Apéry set, which exhibits symmetric appearances.