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HOLYBIBLETHE
  • Member for 9 years, 11 months
  • Last seen more than 4 years ago
  • India
22 votes
8 answers
10k views

If $a$, $a+2$ and $a+4$ are prime numbers then, how can one prove that there is only one solution for $a$? [duplicate]

9 votes
8 answers
4k views

Integrating $\int_0^\infty\frac{1}{1+x^6}dx$

7 votes
2 answers
526 views

How to integrate, $\int_{0}^{\pi/2}\sin (\tan\theta) \mathrm{d\theta}$?

7 votes
6 answers
385 views

Prove that $(n+\sqrt{n^2 -1})^k$ will always be of the form$ (t+\sqrt{t^2 -1})$ where $n$, $k$, $t$ are natural numbers

7 votes
1 answer
2k views

factorise, $x^3-13x^2+32x+20$

6 votes
4 answers
132 views

Consider a function $f(x) = x^4+x^3+x^2+x+1$, where x is an integer, $x\gt 1$. What will be the remainder when $f(x^5)$ is divided by $f(x)$?

5 votes
6 answers
1k views

how can one solve for $x$, $x =\sqrt{2+\sqrt{2+\sqrt{2\cdots }}}$ [duplicate]

5 votes
3 answers
98 views

Is this solution correct?

4 votes
3 answers
14k views

Given digits $2,2,3,3,4,4,4,4$ how many distinct $4$ digit numbers greater than $3000$ can be formed?

4 votes
6 answers
638 views

Does the following series converge?

3 votes
6 answers
2k views

What is the remainder when $25^{889}$ is divided by 99?

3 votes
2 answers
112 views

To split in to partial fractions, the expression $\frac{1}{x^2(x+a)^2}$

3 votes
2 answers
4k views

Find the rank of the following matrix.

3 votes
1 answer
272 views

$X=(1 + \tan 1^{\circ})(1 + \tan 2^{\circ})(1 + \tan 3^{\circ})\ldots(1 + \tan {45}^{\circ})$. what is the value of X? [duplicate]

3 votes
3 answers
125 views

How do we integrate, $\int \frac{1}{x+\frac{1}{x^2}}dx$?

3 votes
4 answers
1k views

how can one find the value of the expression, $(1^2+2^2+3^2+\cdots+n^2)$ [duplicate]

3 votes
1 answer
133 views

Consider $x = (2+\sqrt[]{3})^6$, $x=[x]+t$, where $[x]$ is the integer part of $x$, and $t$ is the 'non integer' part of $x$. find $x(1-t)$

3 votes
3 answers
273 views

$t=\frac{30^{65}-29^{65}}{30^{64}-29^{64}}$, find the closest pair of integers, a and b, such that, $a \lt t \lt b$.

3 votes
1 answer
3k views

If $w=f(z)=u+iv$, is analytic in a region R, then does $\frac{dw}{dz}=\frac{\partial w}{\partial x}=-i\frac{\partial w}{\partial y}$ hold?

3 votes
3 answers
24k views

What is the residue of $f(z)=\tan{z}$ at any of its pole ? Is the solution correct?

2 votes
2 answers
13k views

Show that the function, $f(z)=e^{y}e^{ix}$ is nowhere analytic.

2 votes
1 answer
214 views

Is, $\frac{d f}{d z}\frac{\partial z}{\partial \theta}=\frac{\partial f}{\partial z}\frac{\partial z}{\partial \theta}$?

2 votes
2 answers
505 views

If the roots of the quadratic equation $2kx^{2}+(4k-1)x+2k-3=0$ are rational and k is an integer, how many values can k take which are less that 50?

2 votes
4 answers
975 views

How many values of $n<50$ exist that satisfy$ (n-1)! \ne kn$ where n,k are natural numbers?

2 votes
2 answers
171 views

$f(n)=7^{6n} - 6^{6n}$, where $n$ is a positive integer.

2 votes
4 answers
185 views

$\frac{1}{x}+\frac{4}{y} = \frac{1}{12}$, where $y$ is and odd integer less than $61$. Find the positive integer solutions (x,y).

2 votes
3 answers
285 views

Is there a reasoning behind the depiction of the numbers as they are $\{1$, $2$, $3$, $4$, $5$, $6$, $7$, $8$, $9\}$?

2 votes
4 answers
395 views

can one derive the $n^{th}$ term for the series, $u_{n+1}=2u_{n}+1$,$u_{0}=0$, $n$ is a non-negative integer

2 votes
6 answers
301 views

I know that, $S_{2n}+4S_{n}=n(2n+1)^2$. Is there a way to find $S_{2n}$ or $S_{n}$ by some mathematical process with just this one expression?

2 votes
1 answer
217 views

How many students turned up for renting the rooms?