User Shivam Patel

30 votes

4 answers

11k views

Two circles inside a right angled triangle!

asked Mar 22, 2014 at 6:11

30 votes

3 answers

892 views

A closed form for a lot of integrals on the logarithm

asked Jun 17, 2014 at 6:51

27 votes

2 answers

1k views

Proof of $\sum_{n=1}^{\infty}\frac1{n^3}\frac{\sinh\pi n\sqrt2-\sin\pi n\sqrt2}{{\cosh\pi n\sqrt2}-\cos\pi n\sqrt2}=\frac{\pi^3}{18\sqrt2}$

asked Oct 12, 2013 at 15:19

17 votes

2 answers

25k views

Derivation of formula for finding median for grouped data

asked Oct 25, 2013 at 16:17

14 votes

1 answer

495 views

Are there infinitely many primes $p$ such that $\frac{(p-1)! +1}{p}$ is prime?

asked Dec 28, 2013 at 17:44

14 votes

1 answer

1k views

Extensions of Ramanujan's Cos/Cosh Identity

asked Oct 7, 2013 at 5:50

9 votes

5 answers

660 views

What is different ways to prove that $\sqrt p$ is irrational when $p$ is prime?

asked Oct 17, 2013 at 11:35

9 votes

2 answers

2k views

The Best Problems by Martin Gardner

asked Oct 6, 2014 at 6:33

9 votes

1 answer

575 views

More identities of the Ramanujan Double factorial type.

asked Jan 29, 2014 at 13:14

8 votes

3 answers

1k views

Functions in the Ramanujan master Theorem.

asked Sep 26, 2013 at 8:33

8 votes

1 answer

1k views

On a constant defined by Ramanujan.

asked Jan 13, 2014 at 15:22

7 votes

2 answers

460 views

On the numbers divisible by all the Integers not exceeding their $r^{th}$ roots.

asked May 19, 2014 at 11:14

5 votes

0 answers

2k views

In the Hunt for Kaprekar's Constants for more than 4 digits.

asked Nov 15, 2013 at 5:08

5 votes

1 answer

612 views

My conjecture on almost integers.

asked Oct 20, 2013 at 12:54

4 votes

1 answer

564 views

Representation of integers as powers of the golden ratio

asked Jan 14, 2014 at 6:16

4 votes

2 answers

323 views

A formula for the least common multiple less than n?

asked Sep 24, 2013 at 14:02

4 votes

1 answer

400 views

Integral Representations of Ramanujan theta functions

asked Oct 12, 2013 at 11:12

4 votes

1 answer

300 views

Proof of Infinite Primes in the form $10^{\lceil k \log_{10}(n) \rceil }+n^{k-1}$

asked May 21, 2014 at 4:45

4 votes

1 answer

90 views

On the sum of relatively prime number $<N$

asked May 19, 2014 at 6:29

4 votes

2 answers

336 views

A conjecture on $\phi(n)$

asked Jan 10, 2014 at 8:41

4 votes

1 answer

464 views

Geometric proof of this property of the ellipse

asked Mar 23, 2015 at 6:17

4 votes

0 answers

57 views

On the probability of singular matrices containing whole numbers

asked Apr 25, 2015 at 17:17

4 votes

1 answer

81 views

Infinite Perfect power of numbers in a certain form

asked Jun 17, 2014 at 17:52

3 votes

1 answer

330 views

On combining $n$ and $n^2$ into one number

asked Jun 7, 2014 at 15:56

3 votes

2 answers

123 views

Convincing that $\sum_{n=0}^{\infty}\frac{(-1)^n}{2^{n-2}(2n+1)(n!)} \ne \pi$

asked Mar 25, 2015 at 6:45

3 votes

2 answers

914 views

Magic Squares with Lucas and Fibonacci Numbers

asked May 9, 2014 at 10:19

3 votes

0 answers

88 views

All those unit fractions add to 1?

asked May 22, 2014 at 3:53

3 votes

4 answers

220 views

Evaluation of a particular type of integral involving logs and trigonometric function

asked Jan 20, 2014 at 8:31

3 votes

1 answer

607 views

A visual proof of - Curved surface area of a hemisphere = 2(Area of circle)

asked Dec 12, 2013 at 9:32

3 votes

2 answers

202 views

Proof of my conjecture on closed form of $\int _{0}^{\infty}\frac{x^{a-1}e^{-mbx}}{1-e^{-bx}}$

asked Oct 23, 2013 at 5:30

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74 Questions

Two circles inside a right angled triangle!

A closed form for a lot of integrals on the logarithm

Proof of $\sum_{n=1}^{\infty}\frac1{n^3}\frac{\sinh\pi n\sqrt2-\sin\pi n\sqrt2}{{\cosh\pi n\sqrt2}-\cos\pi n\sqrt2}=\frac{\pi^3}{18\sqrt2}$

Derivation of formula for finding median for grouped data

Are there infinitely many primes $p$ such that $\frac{(p-1)! +1}{p}$ is prime?

Extensions of Ramanujan's Cos/Cosh Identity

What is different ways to prove that $\sqrt p$ is irrational when $p$ is prime?

The Best Problems by Martin Gardner

More identities of the Ramanujan Double factorial type.

Functions in the Ramanujan master Theorem.

On a constant defined by Ramanujan.

On the numbers divisible by all the Integers not exceeding their $r^{th}$ roots.

In the Hunt for Kaprekar's Constants for more than 4 digits.

My conjecture on almost integers.

Representation of integers as powers of the golden ratio

A formula for the least common multiple less than n?

Integral Representations of Ramanujan theta functions

Proof of Infinite Primes in the form $10^{\lceil k \log_{10}(n) \rceil }+n^{k-1}$

On the sum of relatively prime number $<N$

A conjecture on $\phi(n)$

Geometric proof of this property of the ellipse

On the probability of singular matrices containing whole numbers

Infinite Perfect power of numbers in a certain form

On combining $n$ and $n^2$ into one number

Convincing that $\sum_{n=0}^{\infty}\frac{(-1)^n}{2^{n-2}(2n+1)(n!)} \ne \pi$

Magic Squares with Lucas and Fibonacci Numbers

All those unit fractions add to 1?

Evaluation of a particular type of integral involving logs and trigonometric function

A visual proof of - Curved surface area of a hemisphere = 2(Area of circle)

Proof of my conjecture on closed form of $\int _{0}^{\infty}\frac{x^{a-1}e^{-mbx}}{1-e^{-bx}}$