Unified Hybrid Method for Testing Divisibility by Prime Numbers in the Decimal Base

This work introduces a unified framework for divisibility criteria in arithmetic, based on iterative transformations that preserve modular equivalence with respect to a divisor d. Unlike traditional rules, which are presented separately for each divisor (2, 3, 5, 7, 11, etc.), this method relies on a single underlying principle: the decimal reduction of an integer through a transformation invariant modulo d.