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Shivam Patel's user avatar
Shivam Patel's user avatar
Shivam Patel's user avatar
Shivam Patel
  • Member for 10 years, 10 months
  • Last seen more than a week ago
  • India
30 votes
4 answers
12k views

Two circles inside a right angled triangle!

30 votes
3 answers
921 views

A closed form for a lot of integrals on the logarithm

27 votes
2 answers
1k views

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

19 votes
2 answers
26k views

Derivation of formula for finding median for grouped data

14 votes
1 answer
507 views

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

14 votes
1 answer
1k views

Extensions of Ramanujan's Cos/Cosh Identity

9 votes
2 answers
3k views

The Best Problems by Martin Gardner

9 votes
1 answer
595 views

More identities of the Ramanujan Double factorial type.

8 votes
3 answers
1k views

Functions in the Ramanujan master Theorem.

8 votes
5 answers
665 views

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

8 votes
1 answer
1k views

On a constant defined by Ramanujan.

7 votes
2 answers
469 views

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

5 votes
1 answer
485 views

Geometric proof of this property of the ellipse

5 votes
0 answers
2k views

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

5 votes
1 answer
626 views

My conjecture on almost integers.

4 votes
1 answer
612 views

Representation of integers as powers of the golden ratio

4 votes
2 answers
345 views

A formula for the least common multiple less than n?

4 votes
1 answer
421 views

Integral Representations of Ramanujan theta functions

4 votes
0 answers
58 views

On the probability of singular matrices containing whole numbers

4 votes
1 answer
88 views

Infinite Perfect power of numbers in a certain form

4 votes
1 answer
303 views

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

4 votes
1 answer
91 views

On the sum of relatively prime number $<N$

4 votes
2 answers
339 views

A conjecture on $\phi(n)$

3 votes
2 answers
957 views

Magic Squares with Lucas and Fibonacci Numbers

3 votes
0 answers
89 views

All those unit fractions add to 1?

3 votes
1 answer
351 views

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

3 votes
2 answers
123 views

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

3 votes
4 answers
220 views

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

3 votes
1 answer
645 views

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

3 votes
2 answers
202 views

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