Maisam Hedyelloo

3,385 reputation

327

bio	website	mathoverflow.blogfa.com
	location	Iran
	age	22
visits	member for	7 months
	seen	2 mins ago
stats	profile views	905

undergraduate student of mathematics and im interest in pure and applied math like real analysis dynamical system linear algebra and other

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	3,385 reputation	bio	website	mathoverflow.blogfa.com	visits	member for	7 months
327 badges		location	Iran		seen	2 mins ago

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87 Questions

views newest activity votes

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449

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How to prove that $\frac{(5m)!(5n)!}{(m!)(n!)(3m+n)!(3n+m)!}$ is a natural number?

homework elementary-number-theory

apr 30 at 7:56 Mark Hurd 372

votes

answers

199

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How to prove summation, multiplication, subtraction of two roots of $1+x+\frac{x^2}{2!}+\cdots+\frac{x^p}{p!}=0$ aren't rationals?

mar 2 at 10:13 YACP 9,020

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answers

459

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How to prove that $\frac{(mn)!}{m!(n!)^m}$ is an integer?

homework elementary-number-theory

feb 23 at 22:22 Community♦ 1

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674

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If $f''(x)+f(x)>0$ and $f(x)>0$ $\forall x\in(a,b)$; $f(a)=f(b)=0$; prove that $b-a>\pi$.

calculus analysis differential-equations contest-math

jan 18 at 4:20 Landscape 7,700

votes

answer

187

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How to compute the series $\sum\limits_{x=0}^\infty\sum\limits_{y=0}^\infty\sum\limits_{z=0}^\infty\frac{1}{2^x(2^{x+y}+2^{x+z}+2^{z+y})}$

sequences-and-series contest-math

mar 23 at 17:01 Did 102k

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answers

178

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How to find the limit of these sequences?

calculus limit contest-math

may 10 at 9:48 Sami Ben Romdhane 8,091

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117

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how to solve $1!+2!+3!+…+x!=y^{z+1}$where $x,y,z\in \mathbb N$?

homework elementary-number-theory

apr 5 at 20:29 agustin 422

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answers

115

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how prove $n! \mid \prod_{k=0}^{n-1}(2^n-2^k) :\forall n \in \mathbb N$?

number-theory contest-math

mar 19 at 23:12 anon 39.8k

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answers

218

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Proving $x^x+y^y\ge\sqrt2$ when $x,y\in \mathbb R^+$ and $x+y=1$

analysis inequality

feb 4 at 2:25 Michael Li 542

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answer

118

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How to integrate $\int_0^{\pi/2}\frac{\sin^nx}{\sin^nx+\cos^nx}dx$? [duplicate]

integral

feb 1 at 20:36 André Nicolas 161k

votes

answer

151

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how prove the following statment for this matrix.

linear-algebra matrices

jan 30 at 11:15 user1551 16.6k

votes

answers

146

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How to prove that a group with some properties is abelian?

homework abstract-algebra group-theory

mar 11 at 20:14 Nicky Hekster 2,677

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answers

views

How to prove there is no positive and continuous function satisfying some conditions

analysis contest-math

mar 1 at 4:01 Ragib Zaman 17.8k

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108

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Let the matrix $A=[a_{ij}]_{n×n}$ be defined by $a_{ij}=\gcd(i,j )$. How prove that $A$ is invertible, and compute $\det(A)$?

matrices contest-math

feb 10 at 20:44 Sanchez 4,303

votes

answers

159

views

How to prove $n$ is prime?

elementary-number-theory

may 10 at 20:45 Jose Garcia 1,806

votes

answer

117

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$f:[a,b]\to(a,b)$ be continuous how prove $f(c)+f(c+d)+\cdots+f(c+nd)=(n+1)(c+\frac{nd}{2})$

real-analysis analysis continuity contest-math

mar 14 at 10:29 Davide Giraudo 56.2k

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answers

177

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how to prove $G_1$ and $G_2$ aren't isomorphic?

homework abstract-algebra

mar 5 at 21:18 Andreas Caranti 15.1k

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answer

views

How to prove that exists distinct $x_1,x_2 \in(a,b)$ such that $f '(x_1)f '(x_2)=1$?

homework analysis contest-math

feb 11 at 19:26 Ehsan M. Kermani 3,334

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answers

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let$ G=\{M_1,M_2,…,M_k\}$ be a finite group if $\sum _{i=0}^k \operatorname{tr} (M_i)=0$ then how prove $\sum _{i=0}^k M_i=0$

linear-algebra group-theory contest-math

apr 30 at 2:33 julien 22.7k

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answer

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How to prove $\sum_{i=1}^{n-1}\frac{1}{\operatorname{lcm}(a_i,a_{i+1})}\lt1$ where $a_i\in\mathbb N$ and $a_i\lt a_{i+1}$?

homework sequences-and-series number-theory elementary-number-theory inequality

mar 31 at 21:55 Eric♦ 33.2k

votes

answer

163

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how to prove $\sum _{|k|\lt\sqrt m}\binom{2m}{m+k}\ge2^{2m-1}$

homework probability combinatorics contest-math

mar 22 at 22:13 user17762 76.1k

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answer

views

question about limit and series

sequences-and-series analysis contest-math

mar 14 at 0:14 alex.jordan 8,759

votes

answers

109

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If $f:\mathbb{R}\to\mathbb{R}$ is continuous and $[a,b]\subset f([c,d])$, how to prove there is some $[r,s]$ such that $f([r,s])=[a,b]$?

real-analysis general-topology analysis contest-math

mar 7 at 23:05 julien 22.7k

votes

answer

106

views

how prove that $|f(x)|\ge2^n (n+1) $ under these conditions?

analysis integral

jan 28 at 22:00 Matemáticos Chibchas 1,554

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answers

views

let $A,B\in M_{n}(C)$ such that c is complex field and $AB^2-B^2A=B$ how prove $B^n=0$

homework linear-algebra contest-math

jan 25 at 6:39 user1551 16.6k

votes

answers

169

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how to prove this question about derivative and differentiation

analysis contest-math

may 12 at 5:04 Community♦ 1

votes

answers

129

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How to prove that for all $m,n\in\mathbb N$, $\ 56786730 \mid mn(m^{60}-n^{60})$?

homework elementary-number-theory modular-arithmetic divisibility

apr 2 at 19:10 Community♦ 1

votes

answers

108

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The roots of the derivative $P'(z)$ of the polynomial $P(z)\in\mathbb C[x]$ lie in the convex hull of the set of roots of $P(z)$.

complex-numbers contest-math

mar 19 at 20:21 P.. 8,860

votes

answers

111

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let $A\in M{_n}\ (\mathbb R)$ s.t $A^2=I$ such that $A\neq I$, $A\neq -I$ how prove $-(n-1)\le tr A\le n-1$

linear-algebra

feb 15 at 8:47 P.. 8,860

votes

answer

121

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how compute $a_n$ respect to b?

sequences-and-series analysis

feb 7 at 19:29 Christian Blatter 32.5k