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sirous
  • Member for 10 years, 2 months
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  • Tehran iran
12 votes
1 answer
13k views

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

6 votes
1 answer
235 views

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

3 votes
2 answers
334 views

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

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?

3 votes
1 answer
69 views

Construct a triangle with known base and vertex on a hyperbola

3 votes
2 answers
212 views

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

3 votes
1 answer
289 views

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

2 votes
7 answers
279 views

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

2 votes
1 answer
203 views

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

2 votes
2 answers
209 views

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

2 votes
3 answers
482 views

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

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]

2 votes
0 answers
35 views

Geometric solutions for some particular sequences

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?

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 $a+c=n^2$

1 vote
1 answer
146 views

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

1 vote
2 answers
140 views

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

1 vote
0 answers
71 views

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

1 vote
1 answer
116 views

In triangle ABC prove two lines are perpendicular.

1 vote
1 answer
82 views

Prove the solutions of Diophantine equation are limited

1 vote
2 answers
88 views

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

1 vote
1 answer
54 views

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

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]

1 vote
1 answer
58 views

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

1 vote
1 answer
270 views

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

1 vote
1 answer
177 views

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

1 vote
3 answers
163 views

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

1 vote
1 answer
146 views

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

1 vote
2 answers
161 views

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

1 vote
3 answers
123 views

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