# prime number

## Problems for the Senior School July 2019

Some problems for the Senior School.

## Problems for the Senior School - March 2019

Some problems for the Senior School.

## A Pythagoras-style Diophantine Equation and its Solution

The Pythagorean equation x^2 + y^2 = z^2 (to be solved over the positive integers N) is a much-studied one; many articles have appeared in this magazine alone, devoted to this equation. A close relative to this is the equation 1/x + 1/y = 1/z (which can be written as x^−1 + y^−1 = z^−1 ; in this form, its similarity to the Pythagorean equation is readily seen), and this too has been studied many times in At Right Angles.

## There are Infinitely many Prime Numbers

Some theorems, it seems, are evergreen. New proofs keep turning up for them. One such is the theorem of Pythagoras (the current number of proofs stands at over 300). Another is the claim that the square root of 2 is irrational. A third example is the statement that there exist infinitely many prime numbers. This is the one on which we will dwell in this short article.

## Will my turn come?

When something is being passed around, children are always anxious to see when their own turn would come. This activity utilizes that excitement.

## AtRiA: Problems for the Senior School - July 2013

Here are some problems for students in Senior School, edited by Prithwijit De and Shailesh Shirali. The solutions to problems posed will appear in the next issue of AtRiA's problem corner.

## Set Theory Revisited- As easy as PIE Part 2

In Part–II of 'As easy as Pie'  B Sury uses the PIE to find a generalization of the formula connecting the gcd and lcm of two numbers.

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