prime number

Some problems for the Senior School.

Some problems for the Senior School.

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.

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.

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

 

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.

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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