# divisibility

In this edition of ‘Adventures’ we study a few miscellaneous problems, mostly from the Pre-Regional Mathematics Olympiad (PRMO; this year’s PRMO was conducted on August 19 in centres all over the country). As usual, we pose the problems first and present solutions later.

## Problems for the MIDDLE SCHOOL Problems Related to Divisibility

Factors and multiples, tables and long division – students who are relieved at mastering these in numbers are confounded when the same topics rear their head in algebra. Here is a nice collection of problems that allow students to play with algebraic expressions and study them through the lens of divisibility.

## On divisibility by 27

Is there any test for divisibility by 27?

## Problems for the Middle School

Invite your middle school students to this set of problems.

## A Property of Primitive PYTHAGOREAN TRIPLES

Check this Student Corner – Featuring articles written by students.

## Divisibility by Primes

Divisibility tests by primes such as 7, 13, 17 and 19 are not generally discussed in the school curriculum. However, in Vedic Mathematics (also known by the name “High Speed Mathematics”; see Box 1), techniques for testing divisibility by such primes are discussed, but without giving any proofs. In this article, proofs of these techniques are discussed.

## Problems for the Middle School

We hope that you enjoyed the reworked Middle Problems and found the Handy Reference Sheet useful. This time we will continue to focus on parity with some nice problems which use the properties given in the sheet.

## Problems for the Middle School

Pose these to the middle school students.

## A New Test for Divisibility by 8

Check this divisibility test for eight.