I have published a new post on my blog with an explanation of how osculation works in divisibility tests. I had published a Vedic Mathematics lesson on divisibility tests a while back, and followed that up with a lesson on the Vedic Mathematics concept of osculation. The application of osculation using natural osculators (vestanas) leads directly to some of the divisibility tests, especially for numbers that many people don’t even know have divisibility tests.
In this latest post, I examine the relationship between osculation and the modulus operator. The combination of osculation with some properties of the modulus operator, as explained in this post help us derive the divisibility tests that are based on natural osculators. In addition, once these interactions are understood, you can independently derive numerous divisibility tests for practically any number you can think of, some of them based on osculation, others based on other manipulations of the digits of the dividend. You can read all about this and get started deriving your own divisibility tests by reading my post here!