I have been gone for long and also haven’t been having much time on my hands for writing new posts but starting today, I will try to change that and be more frequent in my blogging and present new articles form whatever I am reading and various other articles that interest me.
Recently I came across a particularly fascinating divisibility test for 7 in the blog of Tanya Khovanova who’s quite famous among the math blogging community.
Here is the post :http://blog.tanyakhovanova.com/?p=159
It basically gives you a graph that;s constructed by a certain David Wilson, a fan of sequences who happened to be a guest blogger on the blog i mentioned above.
The main point of the test is as follows :
By David Wilson :
I have attached a picture of a graph.
Write down a number n. Start at the small white node at the bottom of the graph. For each digit d in n, follow d black arrows in a succession, and as you move from one digit to the next, follow 1 white arrow.
For example, if n = 325, follow 3 black arrows, then 1 white arrow, then 2 black arrows, then 1 white arrow, and finally 5 black arrows.
If you end up back at the white node, n is divisible by 7.
Now this made me look out for any other possible interesting ways to test the divisibility by 7 and that is ofcourse keeping in mind that the method i come across should be simpler then direct division process ;).
Another process that has been described in this paper is pretty simple nd staright forward but just a starting point in the author’s idea of divisibility by primes. Do give it a look if you are interested.