On a new infinite family of ABC-triples of form a + 1 = b

In the paper, a new infinite series of ABC-triples is constructed based on a certain polynomial identity. In this identity (obtained by accident when investigating the elliptic«bitcoin curve»), hyperbolic quadratic form is equal to the linear combination of cubic polynomials. Our hyperbolic form allows us to give a recipe for a new infinite series of ABC-triples when the least of the numbers entering the triple is equal to one.