User Sameer Kailasa

39 votes

A Gift Problem for the Year 2018

answered Jan 23, 2018 at 15:29

21 votes

Accepted

How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?

answered May 8, 2015 at 3:59

20 votes

Equation with solution in prime numbers

answered Sep 29, 2017 at 16:09

17 votes

Accepted

Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

answered Jul 31, 2018 at 0:14

17 votes

Prove that the Lie derivative of a vector field equals the Lie bracket: $\frac{d}{dt} ((\phi_{-t})_* Y)|_{t=0} = [X,Y]$

answered Mar 21, 2018 at 19:00

16 votes

Accepted

"Length" of rationals in an interval

answered Apr 24, 2015 at 10:44

16 votes

Accepted

any $2$-dimensional rep of a finite, non-abelian simple group is trivial

answered Dec 20, 2014 at 2:59

15 votes

Accepted

Rows of a Matrix is divisible by 19, show that its Determinant is also divisible by 19

answered Aug 3, 2018 at 19:16

10 votes

Accepted

Prove series form of fractional harmonic numbers

answered Dec 26, 2017 at 19:34

9 votes

Accepted

Sequence of non-constant integer polynomials whose limit is constant

answered Jan 19, 2021 at 13:25

9 votes

Accepted

Solve $\int_{0}^{1} \log(x)\log(1-x) dx$ without convolution

answered May 9, 2015 at 8:12

9 votes

Reference request for Geometric Group Theory

answered Mar 31, 2018 at 18:52

8 votes

Prove that if V is finite dimensional then V is even dimensional?

answered Apr 4, 2017 at 13:19

8 votes

Prove that a martingale bounded in $L_2$ converges almost surely

answered May 12, 2015 at 5:07

8 votes

Accepted

Name for Theorem 3.27 from baby Rudin?

answered Jan 2, 2015 at 0:58

8 votes

Group theory question. If $m$ and $n$ are relatively prime, and $a$, $b$ belong to group and $a^m = b^m$ and $a^n = b^n$, how would one prove $a = b$?

answered Oct 3, 2017 at 15:50

7 votes

Prove that $n$ divides $\phi(a^n-1)$, where $\phi$ is Euler's $\phi$-function.

answered Jun 25, 2014 at 1:29

7 votes

Accepted

Best way to show $\cfrac{1}{1+x^2}$ is a contraction?

answered Jun 20, 2015 at 0:09

7 votes

Proving Binomial Identity without calculus

answered Apr 15, 2018 at 1:34

6 votes

Accepted

Prove if $A$ is a symmetric matrix with real entries, then the eigenvalues of $A$ are real.

answered May 1, 2015 at 3:30

6 votes

Prove that every convergent sequence has a monotone subsequence

answered May 5, 2015 at 2:56

6 votes

$2^b-1$ does not divide $2^a+1$,how can I show it?

answered Jun 11, 2014 at 23:08

6 votes

Question on series till 2009

answered Dec 27, 2014 at 15:41

6 votes

Accepted

Given $\frac{(a-b)(b-c)(a-c)}{(a+b)(b+c)(c+a)}=\frac{1}{11}$. Find $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}.$

answered Oct 7, 2017 at 17:31

6 votes

British Maths Olympiad (BMO) 2002 Round 1 Question 3 Proof without Cauchy-Schwarz?

answered Apr 28, 2018 at 18:31

5 votes

calculate $\int_0^\pi\frac {dx}{1+\sin^2x}$

answered Apr 14, 2018 at 21:31

5 votes

Accepted

Is There any quasi-isomorphism between $\mathbb{R}$ and $\mathbb{R}^2$?

answered Feb 19, 2018 at 6:55

5 votes

Accepted

How many $k$ tuples of subsets $S_1,...,S_k$ are there such that $S_1 \cap ..... \cap S_k = \emptyset $.

answered Mar 2, 2017 at 18:48

5 votes

Accepted

Expected value of number of steps until range reduced to a given fraction

answered Dec 9, 2019 at 22:21

5 votes

How to prove $\sqrt{(a-1)(b-1)}+\sqrt{(a-1)(c-1)}+\sqrt{(b-1)(c-1)}\geq a+b+c+\sqrt{ab}+\sqrt{ac}+\sqrt{bc}$?

answered Dec 12, 2019 at 20:36

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139 Answers

A Gift Problem for the Year 2018

How do I solve this improper integral: $\int_{-\infty}^\infty e^{-x^2-x}dx$?

Equation with solution in prime numbers

Putnam 2007 A5: Finite group $n$ elements order $p$, prove either $n=0$ or $p$ divides $n+1$

Prove that the Lie derivative of a vector field equals the Lie bracket: $\frac{d}{dt} ((\phi_{-t})_* Y)|_{t=0} = [X,Y]$

"Length" of rationals in an interval

any $2$-dimensional rep of a finite, non-abelian simple group is trivial

Rows of a Matrix is divisible by 19, show that its Determinant is also divisible by 19

Prove series form of fractional harmonic numbers

Sequence of non-constant integer polynomials whose limit is constant

Solve $\int_{0}^{1} \log(x)\log(1-x) dx$ without convolution

Reference request for Geometric Group Theory

Prove that if V is finite dimensional then V is even dimensional?

Prove that a martingale bounded in $L_2$ converges almost surely

Name for Theorem 3.27 from baby Rudin?

Group theory question. If $m$ and $n$ are relatively prime, and $a$, $b$ belong to group and $a^m = b^m$ and $a^n = b^n$, how would one prove $a = b$?

Prove that $n$ divides $\phi(a^n-1)$, where $\phi$ is Euler's $\phi$-function.

Best way to show $\cfrac{1}{1+x^2}$ is a contraction?

Proving Binomial Identity without calculus

Prove if $A$ is a symmetric matrix with real entries, then the eigenvalues of $A$ are real.

Prove that every convergent sequence has a monotone subsequence

$2^b-1$ does not divide $2^a+1$,how can I show it?

Question on series till 2009

Given $\frac{(a-b)(b-c)(a-c)}{(a+b)(b+c)(c+a)}=\frac{1}{11}$. Find $\frac{a}{a+b}+\frac{b}{b+c}+\frac{c}{c+a}.$

British Maths Olympiad (BMO) 2002 Round 1 Question 3 Proof without Cauchy-Schwarz?

calculate $\int_0^\pi\frac {dx}{1+\sin^2x}$

Is There any quasi-isomorphism between $\mathbb{R}$ and $\mathbb{R}^2$?

How many $k$ tuples of subsets $S_1,...,S_k$ are there such that $S_1 \cap ..... \cap S_k = \emptyset $.

Expected value of number of steps until range reduced to a given fraction

How to prove $\sqrt{(a-1)(b-1)}+\sqrt{(a-1)(c-1)}+\sqrt{(b-1)(c-1)}\geq a+b+c+\sqrt{ab}+\sqrt{ac}+\sqrt{bc}$?