Ishaan94
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Questions Asked

Ishaan94:
Assume an \(8\times 8\) chessboard with usual colouring. You may repaint all the squares of a row or column. The goal is to attain one black…
 updated 10 months ago
 20 replies
 3 Medals
Mathematics

Ishaan94:
Show that the sum\[\sum_{k=1}^n k! \neq m^2\]for any integer m, for \(n\geq4\).
 updated one year ago
 3 replies
 No Medals Yet
Mathematics

Ishaan94:
Find all the integral solutions of the equation \(8y + 11x + 17 =xy\).
 updated one year ago
 14 replies
 2 Medals
Mathematics

Ishaan94:
Period of \(\Large\frac{\cos x}{\sin x}+\frac{\sin x}{\cos x}\)?
 updated one year ago
 16 replies
 No Medals Yet
Mathematics

Ishaan94:
First answer (by Anders) on http://www.quora.com/Mathematics/HowwouldIshowthat49divides8n7n1forallnge0
Can anyone explain i…
 updated one year ago
 29 replies
 2 Medals
Mathematics

Ishaan94:
Problem.
 updated one year ago
 6 replies
 No Medals Yet
Mathematics

Ishaan94:
Total number of integral points lying inside the triangle formed by the lines \(xy=0\) and \(x+y=a\), where \(a\) is any positive integer.
 updated one year ago
 7 replies
 1 Medal
Mathematics

Ishaan94:
Find \(x\).\[\left(2\cdot 7\right)^n+\left(3\cdot 5\right)^n5 \equiv 0 \pmod{x},\quad n\in\mathbb{Z}\]
 updated one year ago
 16 replies
 1 Medal
Mathematics

Ishaan94:
Whom of you can explain it to me?
http://jeremykun.files.wordpress.com/2011/06/triangleproof.png
 updated one year ago
 28 replies
 2 Medals
Mathematics

Ishaan94:
Request for <HTML> Tags.
…
 updated one year ago
 9 replies
 1 Medal
Mathematics

Ishaan94:
\[\mathsf{a,b,c \in \left[0,1\right]}\]\[\mathsf{\text{Prove}\quad\frac{a}{b+c+1} + \frac{b}{a+c+1} + \frac{c}{a+b+1} + \left(1a\right)\lef…
 updated one year ago
 7 replies
 3 Medals
Mathematics

Ishaan94:
Is this function linear?
\[\sum_{k=1}^{n}\left(a  a_1\right)\cdot\left(aa_2\right)\cdots\left(aa_n\right)\]
Where \(a_1,a_2, \ldots, a_n …
 updated one year ago
 13 replies
 2 Medals
Mathematics

Ishaan94:
If \(\large a_1, a_2,a_3,\ldots,a_n\) are real numbers, show that \[\large\sum_{i=1}^{n}\sum_{j=1}^{n}i\cdot j\cdot \cos \left(a_i  a_j\rig…
 updated one year ago
 3 replies
 2 Medals
Mathematics

Ishaan94:
@mukushla
Prove \(ab + bc + ac \ge \sqrt{3abc \left(a+b+c\right)}\).
 updated one year ago
 5 replies
 2 Medals
Mathematics

Ishaan94:
Show that if \(x^4+ax^3+2x^2+bx+1\) has a real solution, then \(a^2+b^2 ≥ 8\).
 updated one year ago
 8 replies
 3 Medals
Mathematics

Ishaan94:
Find all real triples \((x,y, z)\) that satisfy \(x^4+y^4+z^4−4xyz = −1\).
 updated one year ago
 14 replies
 1 Medal
Mathematics

Ishaan94:
Let \(x,y\) and \(z\) be positive real numbers less than 4. Prove that among the numbers\[\frac{1}x + \frac1{4y},\;\frac{1}z + \frac1{4x},…
 updated one year ago
 15 replies
 2 Medals
Mathematics

Ishaan94:
The sum of \(n\) real numbers is zero and the sum of their pairwise products is also zero. Prove that the sum of the cubes of the numbers is…
 updated one year ago
 5 replies
 2 Medals
Mathematics

Ishaan94:
Number of arrangements of the set \(\{a_1,a_2, \ldots, a_{10}\}\), so that \(a_1\) is always ranked above \(a_2\).
 updated one year ago
 17 replies
 2 Medals
Mathematics

Ishaan94:
Number of ways the word 'SUCCESS' can be arranged, such that no two S's and C's are together.
@Zarkon
 updated one year ago
 23 replies
 3 Medals
Mathematics

Ishaan94:
A simple combinatorics problem.
Word 'SUCCESS'. Number of ways such that no two Ss and Cs are together.
 updated one year ago
 24 replies
 4 Medals
Mathematics

Ishaan94:
Prove \(\large 2^{\sqrt2}\) is \(\mathsf{irrational}\).
 updated one year ago
 No Medals Yet
Mathematics

Ishaan94:
Compute \(f'\left(0\right)\). $$\large f\left(x\right) = \int\limits_{\cos x}^{\sin x} e^{t^2+xt}dt.$$
 updated one year ago
 8 replies
 3 Medals
Mathematics

Ishaan94:
Chat Bug >.<
 updated one year ago
 10 replies
 4 Medals
Mathematics

Ishaan94:
Number of ways of distributing \(n\) identical things among \(r\) persons when each person can get any number of things.
@Zarkon
 updated one year ago
 5 replies
 3 Medals
Mathematics

Ishaan94:
The streets of a city are arranged like the lines of a chessboard. Let the dimensions be \(m \times n\). Find the number of ways in which a…
 updated one year ago
 44 replies
 3 Medals
Mathematics

Ishaan94:
How to get fonts work on every OperatingSystem? Like I use ubuntu and windows 7, I have photoshop installed on windows 7. I used adobe photo…
 updated one year ago
 5 replies
 2 Medals
Mathematics

Ishaan94:
How to make dropdown menu with HTML and CSS? Also, if you can then please post your favorite styles, tricks and fonts for web designing.
 updated one year ago
 2 replies
 No Medals Yet
Mathematics

Ishaan94:
Integrate.
\[\large\int\limits_{.9}^{.9}\lfloor x^2\rfloor\;dx\]
 updated one year ago
 3 replies
 No Medals Yet
Mathematics

Ishaan94:
Problem: http://projecteuler.net/problem=2
Solution: …
 updated one year ago
 10 replies
 3 Medals
Mathematics
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