Symbolic Generation and Modular Embedding of High-Quality Abc-Triples

We present a symbolic identity for generating integer triples $a, b, c$ satisfying $a + b = c$, inspired by structural features of the \emphabc conjecture. The construction uses powers of $2$ and $3$ in combination with modular inversion in $\mathbbZ/3^p\mathbbZ$, leading to a parametric identity...