Monthly Archives: February 2015

Bonferroni’s Inequality

Posted on February 11, 2015 by Sumant Sumant

Bonferroni Inequality provides a lower bound for intersection of sets in terms of the individual probability of sets. For sets. It says that for two sets for n sets Main Idea: The union of sets is always smaller than the … Continue reading →

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a+b+3ab

Posted on February 9, 2015 by Sumant Sumant

We saw in sundaram’s sieve and how it gives for any number not present in the sieve gives as prime. The question here is that there are umbels that one cannot be represented as

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Solutions of ab=a+b

Posted on February 9, 2015 by Sumant Sumant

which means

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Equation of factorials

Posted on February 9, 2015 by Sumant Sumant

Show that there is a unique solution to and has infinite many solutions.

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A family of equation

Posted on February 8, 2015 by Sumant Sumant

Show that the equation has a rational root between and for all

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Counting Triangles

Posted on February 8, 2015 by Sumant Sumant

The rods of lengths can be made to form a triangle if and only if the three triangle inequalities are satisfied: . Suppose one wants to make just one triangle and has at his disposal exactly one rod of each … Continue reading →

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Quadruple of consecutive integers

Posted on February 8, 2015 by Sumant Sumant

The numbers are divisible by respectively. Can you find consecutive integers divisible by The numbers will be obviously . Now let’s focus on . Now for a difference to be divisible both the numbers should be divisible by . Which … Continue reading →

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Angle bisector theorem proof -1

Posted on February 8, 2015 by Sumant Sumant

Extend the angle bisector and draw a line parallel to one of the side so that it completes a triangle. This is an isosceles triangle. Here is another proof using only sine rule.  

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On Cubic Curves

Posted on February 7, 2015 by Sumant Sumant

is a point on the graph of . The tangent at crosses the curve at , and is the area between the curve and the segment . Similarly, the tangent at meets the curve again at , and is the … Continue reading →

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Prime number generator

Posted on February 7, 2015 by Sumant Sumant

Suppose the first prime numbers are divided into two groups in any way whatever and the products and of the numbers in the groups determined, an empty set being assigned a product of . Prove that each of the number … Continue reading →

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