## Fun way to learn some basic number theory !!!

A test of divisibility by 3, 7 and 19:

The product of the prime numbers 3, 7 and 19 is 399. If a number $100a+b$ (where b is a two-digit number and a is any positive integer) is  divisible by 399 or by any of its divisors, then $a+4b$ is divisible by the same number.

On your own, can u prove this? (Hint: Use $400a+4b$ as a link). Can you formulate and prove its converse?

Devise a simple test of divisibility by 3, 7 and 19.

More recreational problems in number theory are coming soon !!

Nalin Pithwa

### One Comment

1. Anubhav C. Singh