User sirous - Mathematics Stack Exchange

12 votes

1 answer

13k views

Sum of series : $1+11+111+...$

asked Sep 29, 2016 at 18:45

6 votes

1 answer

235 views

Does equation $a^m+b^n =c^{m+n}$ have integral solutions?

asked Jul 27, 2023 at 10:11

3 votes

2 answers

334 views

Has equation $a^n+b^n=c^n+1$ infinite solutions with $n>2$?

asked Jul 31, 2023 at 19:21

3 votes

0 answers

152 views

Is $N=2^{2^n}+2^{2^{n-1}}+2^{2^{n-2}}+2^{2^{n-3}} + \ldots+ 2^{2^3}+2^{2^2}+n$ is always composite?

asked Aug 23, 2020 at 13:56

3 votes

1 answer

69 views

Construct a triangle with known base and vertex on a hyperbola

asked Feb 24 at 16:32

3 votes

2 answers

212 views

Evaluate $\int x^{x^n+n-1}(x \ln x +1)\mathrm dx$

asked Sep 6, 2018 at 8:02

3 votes

1 answer

289 views

Integration of $\int^{\pi/45}_0 \frac{x^2 \ln (1-x)}{1-x^3}\, dx$

asked Oct 13, 2018 at 7:45

2 votes

7 answers

279 views

Integrate $\int \frac{1}{1+ \tan x}dx$ [duplicate]

asked Jul 26, 2018 at 20:28

2 votes

1 answer

203 views

Find condition for $\alpha + \beta+ \gamma=\alpha . \beta. \gamma$

asked Sep 14, 2018 at 18:04

2 votes

2 answers

209 views

Why numbers of the form $2^{2t} ± 3$ are primes?

asked Feb 22, 2020 at 7:36

2 votes

3 answers

482 views

Is $4\underbrace{999 . . . 9}_{224 ({\rm times})}$ prime?

asked Mar 13, 2020 at 17:05

2 votes

3 answers

430 views

If $x_0=1$ and $x_n=\frac {1}{1+x_{(n-1)}}$, find: $\lim_{x\to\infty} x_n$ [duplicate]

asked Aug 8, 2020 at 7:22

2 votes

0 answers

35 views

Geometric solutions for some particular sequences

asked Aug 5, 2023 at 17:32

1 vote

2 answers

136 views

Can the number of terms of sequence $p_1$, $2p_1+1$, $2(2p_1+1)+1$, . . . be more than 3?

asked Oct 26, 2020 at 16:20

1 vote

3 answers

140 views

Can this problem have solutions for $N>3$:Find three $(N=3)$ positive integers a, b and c such that: $a+b+c=k^2$, $a+b=t^2$, $b+c=m^2$ and $a+c=n^2$

asked Oct 30, 2020 at 10:15

1 vote

1 answer

146 views

Find remainder of $\sum^{2015}_{n=1}\big(\frac{n+2}{2}\big)^{n+2}$ when divided by $23$

asked Aug 7, 2020 at 16:58

1 vote

2 answers

140 views

If $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$, what is minimum of $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$?

asked Mar 4, 2020 at 15:53

1 vote

0 answers

71 views

Sum of decimal digits of primes as a power of a number

asked Jan 10, 2020 at 15:48

1 vote

1 answer

116 views

In triangle ABC prove two lines are perpendicular.

asked Jan 11, 2020 at 8:07

1 vote

1 answer

82 views

Prove the solutions of Diophantine equation are limited

asked Jan 15, 2020 at 15:07

1 vote

2 answers

88 views

If $\cos^{-1}(\frac{x}{a})+\cos^{-1}(\frac{y}{b})=\theta$, then $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{2xy} {ab}\cos(\theta)$

asked Jan 21, 2020 at 18:37

1 vote

1 answer

54 views

Condition for $\frac{1}{x^2}+\frac{1}{2x^4}+\frac{1}{3x^6}+ . . . =\frac{2}{y}+\frac{2}{3y^3}+\frac{2}{5y^5}+ . . .$

asked Jan 23, 2020 at 9:28

1 vote

2 answers

105 views

Inequality $\sqrt{a_1a_2}+\sqrt{a_2a_3}+\cdots+ \sqrt{a_{n-1}a_n}≤ \frac{n-1}{2}(a_1+a_2+ \cdots + a_n)$ [duplicate]

asked Feb 4, 2020 at 20:19

1 vote

1 answer

58 views

On the inequality $a^{1/n}<b^{1/n}+c^{1/n}<d^{1/n}$

asked Feb 6, 2020 at 9:05

1 vote

1 answer

270 views

Solving equation $x^3+x^2+x=1$

asked Sep 20, 2016 at 8:57

1 vote

1 answer

177 views

Value of $A=\sum_{n=2}^\infty\frac1{n^{n-1}}$

asked Sep 24, 2016 at 10:33

1 vote

3 answers

163 views

Integrate $y=\int x^x(\ln x+1)\ dx$

asked Sep 26, 2016 at 5:55

1 vote

1 answer

146 views

Find x and y such that $xx...x6yy...4=k^2$.

asked Nov 16, 2019 at 15:03

1 vote

2 answers

161 views

on $p^n+q^n=(p+q)^k$

asked Dec 31, 2019 at 9:33

1 vote

3 answers

123 views

Is this solution correct for equation $3x^2-4y^2=13$?

asked Jan 7, 2020 at 18:29

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56 Questions

Sum of series : $1+11+111+...$

Does equation $a^m+b^n =c^{m+n}$ have integral solutions?

Has equation $a^n+b^n=c^n+1$ infinite solutions with $n>2$?

Is $N=2^{2^n}+2^{2^{n-1}}+2^{2^{n-2}}+2^{2^{n-3}} + \ldots+ 2^{2^3}+2^{2^2}+n$ is always composite?

Construct a triangle with known base and vertex on a hyperbola

Evaluate $\int x^{x^n+n-1}(x \ln x +1)\mathrm dx$

Integration of $\int^{\pi/45}_0 \frac{x^2 \ln (1-x)}{1-x^3}\, dx$

Integrate $\int \frac{1}{1+ \tan x}dx$ [duplicate]

Find condition for $\alpha + \beta+ \gamma=\alpha . \beta. \gamma$

Why numbers of the form $2^{2t} ± 3$ are primes?

Is $4\underbrace{999 . . . 9}_{224 ({\rm times})}$ prime?

If $x_0=1$ and $x_n=\frac {1}{1+x_{(n-1)}}$, find: $\lim_{x\to\infty} x_n$ [duplicate]

Geometric solutions for some particular sequences

Can the number of terms of sequence $p_1$, $2p_1+1$, $2(2p_1+1)+1$, . . . be more than 3?

Can this problem have solutions for $N>3$:Find three $(N=3)$ positive integers a, b and c such that: $a+b+c=k^2$, $a+b=t^2$, $b+c=m^2$ and $a+c=n^2$

Find remainder of $\sum^{2015}_{n=1}\big(\frac{n+2}{2}\big)^{n+2}$ when divided by $23$

If $\frac{x}{a}+\frac{y}{b}+\frac{z}{c}=1$, what is minimum of $\frac{1}{x^2}+\frac{1}{y^2}+\frac{1}{z^2}$?

Sum of decimal digits of primes as a power of a number

In triangle ABC prove two lines are perpendicular.

Prove the solutions of Diophantine equation are limited

If $\cos^{-1}(\frac{x}{a})+\cos^{-1}(\frac{y}{b})=\theta$, then $\frac{x^2}{a^2}+\frac{y^2}{b^2}-\frac{2xy} {ab}\cos(\theta)$

Condition for $\frac{1}{x^2}+\frac{1}{2x^4}+\frac{1}{3x^6}+ . . . =\frac{2}{y}+\frac{2}{3y^3}+\frac{2}{5y^5}+ . . .$

Inequality $\sqrt{a_1a_2}+\sqrt{a_2a_3}+\cdots+ \sqrt{a_{n-1}a_n}≤ \frac{n-1}{2}(a_1+a_2+ \cdots + a_n)$ [duplicate]

On the inequality $a^{1/n}<b^{1/n}+c^{1/n}<d^{1/n}$

Solving equation $x^3+x^2+x=1$

Value of $A=\sum_{n=2}^\infty\frac1{n^{n-1}}$

Integrate $y=\int x^x(\ln x+1)\ dx$

Find x and y such that $xx...x6yy...4=k^2$.

on $p^n+q^n=(p+q)^k$

Is this solution correct for equation $3x^2-4y^2=13$?