*n*, thus including the prime number cases of

*n*as well. However, do you mean anything else by the 'cases of prime numbers'?

- Fri Mar 08, 2013 7:20 pm
- Forum: Number Theory
- Topic: fermat's last theorem
- Replies:
**4** - Views:
**1934**

Hi Farhan, can you please elaborate your question? Because Fermat's last theorem has been proved for the general case of integer *n*, thus including the prime number cases of *n* as well. However, do you mean anything else by the 'cases of prime numbers'?

- Thu Feb 21, 2013 7:17 pm
- Forum: Combinatorics
- Topic: Probability :Two gamblers
- Replies:
**3** - Views:
**2145**

Does 'Prob of $A$' in your calculation mean the probability of A's winning or the probability of just getting the sum 6 in any throw of the dices? Your conclusion is right, but not the reasoning you provided in your comment, especially because the dice throwing may go on for round after round before...

- Thu Feb 21, 2013 3:54 pm
- Forum: Social Lounge
- Topic: Quadratic Equation
- Replies:
**4** - Views:
**2977**

Dear Prosenjit, your confusion is not unjustified. The equation $x^2+2x+1=0$ does 'in reality' have one root, $-1$. But then $x+1=0$ or $x^3+3x^2+3x+1=0$ has also only one root each, $-1$. To make things logically consistent and to differentiate among these equations in terms of their roots, we say ...

- Tue Feb 19, 2013 11:56 pm
- Forum: Junior Level
- Topic: Help to factorize!
- Replies:
**4** - Views:
**2191**

Dear Abdullah, hope it helps :) $2a^2b^2+2b^2c^2+2c^2a^2-a^4-b^4-c^4$ $=-(a^4+b^4+c^4-2a^2b^2-2b^2c^2-2c^2a^2)$ $=-\left\{(a^4+b^4+c^4-2a^2b^2+2b^2c^2-2c^2a^2)-4b^2c^2\right\}$ $=-\left\{(a^2-b^2-c^2 )^2-(2bc)^2\right\}$ $=-\left\{a^2-b^2-c^2+2bc\right\}\left\{a^2-b^2-c^2-2bc\right\}$ $=-\left\{a^2-...

- Tue Feb 19, 2013 8:31 pm
- Forum: Junior Level
- Topic: Help to factorize!
- Replies:
**4** - Views:
**2191**

@Dear Mahi, perhaps you wrote it in haste and did not look that your factorization would make all the terms negative. The actual factors look like

$(a+b+c)(a+b-c)(c+a-b)(c-a+b)$

$(a+b+c)(a+b-c)(c+a-b)(c-a+b)$

- Thu Feb 07, 2013 4:51 pm
- Forum: Divisional Math Olympiad
- Topic: Rajshahi MO 2013, Secondary 1
- Replies:
**9** - Views:
**3700**

As we can read the actual question in Mehfuj Zahir's comment, the answer is now quite obvious and simple because of the word "at most" in the question. And the answer is $\binom {2013} {4}$, as explained by Mahi and Adib. The formula could be quite complicated if the polygon were regular with even n...

@sowmitra, Your thinking about the whole picture, and about my trouble :), is certainly wrong, because what you explained in your first major paragraphâ€”such as only form of motion, vertical acceleration of Tarzan and bullet, horizontal motion of bullet, no relative vertical motion between them ) bas...

@Dear Mahi: You have either failed to read or grossly misrepresented what I actually wrote, because nowhere in my explanation did I write or mean that the branch height itself is the only parameter to determine the situation, hit vs. no-hit. I clearly wrote that the bullet will hit Tarzan only if bu...

Looking at the given answer choices, we can guess that the people who devised the question would choose (A) as its correct answer. Although (A) is better than the other three, it requires, to be correct, at least one assumption , which is not mentioned in the question. Therefore, if we critically ev...

- Wed Jan 16, 2013 8:18 pm
- Forum: Physics
- Topic: Black Hole
- Replies:
**16** - Views:
**7782**

The notion of time is perhaps the most intriguing thing in human experience. And modern science has only added a new approach to understand, if not successfully explained, the notion. Let us assume that black holes certainly exist with all their unusual properties, including time dilation. Let us fu...