On $p$-adic solubility of $A{x}^{\ell }+B{y}^m+C{z}^n=0$

Santiago Arango-Piñeros, Christopher Keyes, Andrew Kobin

We study $p$-adic solubility of generalized Fermat equations $A{x}^{\ell }+B{y}^m+C{z}^n=0$ for positive integers $\ell ,m,n$. For all but finitely many primes $p$, the probability of…