User user-492177

9 votes

1 answer

333 views

Showing an infinite sequence is constant under some condition

asked Jul 22, 2020 at 7:16

7 votes

3 answers

356 views

If $ (ab)^2=b^2 a^2 , \forall a , b\in G$ , then $G$ is necessarily abelian?

asked Jun 4 at 10:06

7 votes

1 answer

176 views

If $\sum a_n$ is divergent , $b_n \uparrow \infty $ then $\Sigma a_n b_n $ is divergent?

asked Sep 10 at 7:11

6 votes

2 answers

2k views

No continuous injective functions from $\mathbb{R}^2$ to $\mathbb{R}$

asked Dec 27, 2020 at 4:42

6 votes

2 answers

2k views

In a finite commutative ring , every prime ideal is maximal?

asked Aug 29, 2020 at 18:42

6 votes

3 answers

541 views

$Q=(P+\frac12I)$ is invertible where $P$ is a square matrix with integral entries

asked Apr 16, 2020 at 6:26

4 votes

1 answer

120 views

A differential inequality with boundary values

asked Aug 20, 2020 at 6:26

4 votes

2 answers

676 views

A periodic function with no fundamental period and continous at one point is constant.

asked Aug 24, 2020 at 8:19

4 votes

1 answer

320 views

$f\in C [-1,1]$ and $\int_{-1}^1 f(x) x^{2n} dx=0$ implies $f$ is odd function?

asked Sep 22, 2020 at 7:09

4 votes

1 answer

261 views

Edelstein's Version of the Banach Fixed Point Theorem

asked Aug 6, 2020 at 16:38

4 votes

1 answer

407 views

For which $p$, does there exist an anti-derivative?

asked Dec 23, 2020 at 13:48

3 votes

1 answer

234 views

Finding the number of permutations on $\{1,2,3,..,n\}$ under some restrictions

asked Sep 11, 2020 at 10:29

3 votes

1 answer

266 views

Limit points of the set $\{\frac {\varphi(n) }n : n\in \mathbb{N}\}$

asked Dec 29, 2020 at 9:49

3 votes

0 answers

195 views

On the number of permutations on $n$ letters with the greatest cycle length of $k$

asked May 16, 2023 at 19:11

3 votes

1 answer

200 views

About a function bounded by two polynomials

asked Jun 1 at 10:33

3 votes

1 answer

108 views

$\lim_{\epsilon \rightarrow 0} \frac 1{\epsilon} \int_0 ^{\infty} f(x ,\epsilon) dx$

asked Aug 12 at 15:57

3 votes

1 answer

61 views

On a real square matrix of order $10$

asked Jun 18, 2020 at 7:50

3 votes

1 answer

68 views

Open and Closed subset of $\mathbb{R}^n$

asked Jun 25, 2020 at 17:01

3 votes

1 answer

671 views

A finite non cyclic group, all of whose proper subgroups are cyclic, has a non trivial proper normal subgroup.

asked Feb 18, 2020 at 11:28

3 votes

4 answers

557 views

20 balls in 5 different bins, at least 2 per bin

asked Feb 6, 2020 at 12:01

3 votes

1 answer

116 views

Find the sum $\sum _{n=1}^{\infty}a_1a_2a_3...a_n $ where $a_{n+1}=\ln\frac{e^{a_n}-1}{a_n}$.

asked Apr 3, 2020 at 7:46

2 votes

3 answers

79 views

Properties of the set $S=\{f_n(x)=f(x^{1+\frac1n}) : n\in N \} $ where $ f(x)$ is a Lipschitz function in the space $C[0,1]$ with sup norm.

asked Apr 15, 2020 at 7:45

2 votes

1 answer

315 views

A monotone function $f$ on $[0,1]$ satisfying $f\big(\frac14\big)f\big(\frac34\big)\lt 0$

asked May 14, 2020 at 7:35

2 votes

1 answer

251 views

The ideal $\langle x^2+1, y-1 \rangle$ in $\mathbb{Q}[x,y]$

asked May 18, 2020 at 14:33

2 votes

1 answer

390 views

Number of maximal ideals in the ring $\mathbb{Z}_5[x]/\langle (x+1)^2(x+2)^3 \rangle$

asked May 20, 2020 at 12:04

2 votes

1 answer

797 views

Analytic function on an open subset $U$ of $\mathbb{C}$

asked May 23, 2020 at 11:51

2 votes

1 answer

131 views

Why isn't $\{0\}$ being prime ideal is not maximal in $\mathbb{Z}$? [duplicate]

asked May 24, 2020 at 20:47

2 votes

0 answers

123 views

A holomorhic function $f $ in the unit disc such that $\lim_{z\rightarrow 1}f(z)$ does not exist

asked May 25, 2020 at 20:06

2 votes

0 answers

65 views

Polynomials with complex coefficients.

asked May 28, 2020 at 16:41

2 votes

1 answer

1k views

Is $G^2$ necessarily a subgroup of $G$?

asked Jul 5, 2020 at 9:51

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100 Questions

Showing an infinite sequence is constant under some condition

If $ (ab)^2=b^2 a^2 , \forall a , b\in G$ , then $G$ is necessarily abelian?

If $\sum a_n$ is divergent , $b_n \uparrow \infty $ then $\Sigma a_n b_n $ is divergent?

No continuous injective functions from $\mathbb{R}^2$ to $\mathbb{R}$

In a finite commutative ring , every prime ideal is maximal?

$Q=(P+\frac12I)$ is invertible where $P$ is a square matrix with integral entries

A differential inequality with boundary values

A periodic function with no fundamental period and continous at one point is constant.

$f\in C [-1,1]$ and $\int_{-1}^1 f(x) x^{2n} dx=0$ implies $f$ is odd function?

Edelstein's Version of the Banach Fixed Point Theorem

For which $p$, does there exist an anti-derivative?

Finding the number of permutations on $\{1,2,3,..,n\}$ under some restrictions

Limit points of the set $\{\frac {\varphi(n) }n : n\in \mathbb{N}\}$

On the number of permutations on $n$ letters with the greatest cycle length of $k$

About a function bounded by two polynomials

$\lim_{\epsilon \rightarrow 0} \frac 1{\epsilon} \int_0 ^{\infty} f(x ,\epsilon) dx$

On a real square matrix of order $10$

Open and Closed subset of $\mathbb{R}^n$

A finite non cyclic group, all of whose proper subgroups are cyclic, has a non trivial proper normal subgroup.

20 balls in 5 different bins, at least 2 per bin

Find the sum $\sum _{n=1}^{\infty}a_1a_2a_3...a_n $ where $a_{n+1}=\ln\frac{e^{a_n}-1}{a_n}$.

Properties of the set $S=\{f_n(x)=f(x^{1+\frac1n}) : n\in N \} $ where $ f(x)$ is a Lipschitz function in the space $C[0,1]$ with sup norm.

A monotone function $f$ on $[0,1]$ satisfying $f\big(\frac14\big)f\big(\frac34\big)\lt 0$

The ideal $\langle x^2+1, y-1 \rangle$ in $\mathbb{Q}[x,y]$

Number of maximal ideals in the ring $\mathbb{Z}_5[x]/\langle (x+1)^2(x+2)^3 \rangle$

Analytic function on an open subset $U$ of $\mathbb{C}$

Why isn't $\{0\}$ being prime ideal is not maximal in $\mathbb{Z}$? [duplicate]

A holomorhic function $f $ in the unit disc such that $\lim_{z\rightarrow 1}f(z)$ does not exist

Polynomials with complex coefficients.

Is $G^2$ necessarily a subgroup of $G$?