User HOLYBIBLETHE

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]

elementary-number-theory

asked Aug 31, 2012 at 7:20

9 votes

8 answers

4k views

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

asked Jan 31, 2014 at 16:56

7 votes

2 answers

526 views

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

calculus

asked Dec 26, 2012 at 3:38

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

number-theory

asked Aug 3, 2012 at 8:24

7 votes

1 answer

2k views

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

algebra-precalculus polynomials factoring

asked Mar 14, 2013 at 2:10

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 $f(x)$?

algebra-precalculus

asked Jan 24, 2013 at 4:59

5 votes

6 answers

1k views

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

algebra-precalculus nested-radicals

asked Aug 25, 2012 at 6:56

5 votes

3 answers

98 views

Is this solution correct?

systems-of-equations radicals

asked Jul 16, 2013 at 14:15

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?

combinatorics

asked Aug 26, 2012 at 3:40

4 votes

6 answers

638 views

Does the following series converge?

sequences-and-series convergence-divergence

asked Apr 11, 2013 at 5:12

3 votes

6 answers

2k views

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

elementary-number-theory

asked Mar 31, 2013 at 0:31

3 votes

2 answers

112 views

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

fractions partial-fractions

asked May 2, 2013 at 18:35

3 votes

2 answers

4k views

Find the rank of the following matrix.

linear-algebra matrices

asked May 7, 2013 at 14:30

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]

trigonometry

asked Feb 15, 2013 at 1:13

3 votes

3 answers

125 views

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

calculus integration

asked Mar 7, 2013 at 8:53

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]

elementary-number-theory

asked Aug 30, 2012 at 0:11

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 $x(1-t)$

number-theory

asked Aug 4, 2012 at 4:33

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, $a \lt t \lt b$.

combinatorics approximation

asked Aug 21, 2012 at 6:49

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?

complex-analysis

asked Aug 9, 2013 at 6:52

3 votes

3 answers

24k views

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

residue-calculus

asked Jan 29, 2014 at 15:02

2 votes

2 answers

13k views

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

complex-analysis

asked Aug 15, 2013 at 11:55

2 votes

1 answer

214 views

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

partial-derivative

asked Aug 11, 2013 at 9:18

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?

quadratics

asked Aug 13, 2013 at 7:43

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?

factorial

asked Aug 7, 2013 at 13:14

2 votes

2 answers

171 views

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

arithmetic mental-arithmetic

asked Aug 15, 2012 at 13:17

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).

diophantine-equations

asked Aug 15, 2012 at 16:03

2 votes

3 answers

285 views

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

soft-question notation math-history number-systems

asked Aug 22, 2012 at 3:28

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

sequences-and-series arithmetic recurrence-relations

asked Aug 17, 2012 at 11:57

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?

number-theory recurrence-relations

asked Aug 30, 2012 at 6:16

2 votes

1 answer

217 views

How many students turned up for renting the rooms?

recreational-mathematics

asked Aug 25, 2012 at 8:59

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98 Questions

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

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

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

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

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

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 $f(x)$?

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

Is this solution correct?

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

Does the following series converge?

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

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

Find the rank of the following matrix.

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

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

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

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 $x(1-t)$

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

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?

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

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

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

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?

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

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

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

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

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

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?

How many students turned up for renting the rooms?