Search found 57 matches

by SMMamun
Fri Mar 08, 2013 7:20 pm
Forum: Number Theory
Topic: fermat's last theorem
Replies: 4
Views: 1432

Re: fermat's last theorem

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'?
by SMMamun
Thu Feb 21, 2013 7:17 pm
Forum: Combinatorics
Topic: Probability :Two gamblers
Replies: 3
Views: 1674

Re: Probability :Two gamblers

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...
by SMMamun
Thu Feb 21, 2013 3:54 pm
Forum: Social Lounge
Topic: Quadratic Equation
Replies: 4
Views: 2397

Re: Quadratic Equation

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 ...
by SMMamun
Tue Feb 19, 2013 11:56 pm
Forum: Junior Level
Topic: Help to factorize!
Replies: 4
Views: 1634

Re: Help to factorize!

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-...
by SMMamun
Tue Feb 19, 2013 8:31 pm
Forum: Junior Level
Topic: Help to factorize!
Replies: 4
Views: 1634

Re: Help to factorize!

@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
$(a+b+c)(a+b-c)(c+a-b)(c-a+b)$
by SMMamun
Thu Feb 07, 2013 4:51 pm
Forum: Divisional Math Olympiad
Topic: Rajshahi MO 2013, Secondary 1
Replies: 9
Views: 2866

Re: Rajshahi MO 2013, Secondary 1

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...
by SMMamun
Sun Jan 27, 2013 8:37 pm
Forum: Physics
Topic: TARZAN
Replies: 7
Views: 2790

Re: TARZAN

@sowmitra, Your thinking about the whole picture, and about my trouble :), is certainly wrong, because what you explained in your first major paragraph—such as only form of motion, vertical acceleration of Tarzan and bullet, horizontal motion of bullet, no relative vertical motion between them ) bas...
by SMMamun
Sat Jan 26, 2013 6:50 pm
Forum: Physics
Topic: TARZAN
Replies: 7
Views: 2790

Re: TARZAN

@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...
by SMMamun
Mon Jan 21, 2013 9:23 pm
Forum: Physics
Topic: TARZAN
Replies: 7
Views: 2790

Re: TARZAN

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...
by SMMamun
Wed Jan 16, 2013 8:18 pm
Forum: Physics
Topic: Black Hole
Replies: 16
Views: 6170

Black Hole and Time

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...