Search found 37 matches

by Ragib Farhat Hasan
Mon Jan 07, 2019 9:01 pm
Forum: Social Lounge
Topic: How unfortunated we are!
Replies: 2
Views: 523

Re: How unfortunated we are!

Of course we should. And you're right, this forum has turned into a 'death valley', which is very unfortunate. Once this forum was very active, with over 100 posts each day. But sometime in 2017 everybody got more involved with this forum called 'The Art of Problem Solving', and that was the beginni...
by Ragib Farhat Hasan
Fri Oct 19, 2018 2:04 am
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Secondary 2007/12
Replies: 2
Views: 379

Re: BdMO National Secondary 2007/12

$x^2-1=0$
$x^2=1$
$x= +1$ or, $-1$

Let, $f(x)=x^{100}-2x^{51}+1$
Now, the remainder(s) can be found using the Remainder theorem.

When $x=+1$
$f(x)=1-2(1)+1$
$f(x)=0$

When $x=-1$
$f(x)=1-2(-1)+1$
$f(x)=4$
by Ragib Farhat Hasan
Fri Oct 19, 2018 1:49 am
Forum: Primary Level
Topic: Combinatorics
Replies: 6
Views: 929

Re: Combinatorics

The answer should be 14.
by Ragib Farhat Hasan
Fri Oct 19, 2018 1:43 am
Forum: Number Theory
Topic: no solution (a,b)
Replies: 2
Views: 691

Re: no solution (a,b)

There can be another solution to this problem, which includes a bit of messy work of Algebra. $a^2=b^7+7$ $a^2-16=b^7-9$ $(a+4)(a-4)=(\sqrt{b^7}+3)(\sqrt{b^7}-3)$ Now using a little bit of Algebra, it can be shown that there is no integer value of $a$ or, $b$ that satisfies the above equation, hence...
by Ragib Farhat Hasan
Tue Oct 16, 2018 8:01 pm
Forum: Number Theory
Topic: no solution (a,b)
Replies: 2
Views: 691

Re: no solution (a,b)

The LHS of the equation is always positive. So $b>0$, as for $b=0, a= \sqrt7$, and when $b=-1, a=\sqrt6$. And when $b<-1$, the equation becomes invalid. Therefore, it can be deduced that $b>0$. $a^2-b^7=7$ $(a+\sqrt{b^7}) (a-\sqrt{b^7})=7$ Now, $a>b$, otherwise the equation draws into a negative res...
by Ragib Farhat Hasan
Thu Sep 27, 2018 7:31 pm
Forum: Algebra
Topic: Minimum value
Replies: 3
Views: 523

Re: Minimum value

Apparently, the denominators should be 1. So the minimum value will be 6.
by Ragib Farhat Hasan
Mon Sep 03, 2018 8:54 pm
Forum: Higher Secondary Level
Topic: Geometric question...Need help
Replies: 1
Views: 541

Re: Geometric question...Need help

I think the answer is 6.
by Ragib Farhat Hasan
Mon Sep 03, 2018 1:42 am
Forum: Secondary: Solved
Topic: Divisional MO Secondary 2010
Replies: 2
Views: 1730

Re: Divisional MO Secondary 2010

Answer to ques. no. 12 is 201.
by Ragib Farhat Hasan
Mon Sep 03, 2018 1:33 am
Forum: Higher Secondary Level
Topic: A problem of combinatorics
Replies: 9
Views: 1980

Re: A problem of combinatorics

Hint Use function Answer Correct answer $\fbox {3885}$ The correct answer of this problem is 546, and it is an established solution. This problem actually appeared in the National Math Olympiad 2015 in secondary and higher secondary categories. Moreover, read the question again. It says that no one...
by Ragib Farhat Hasan
Mon Sep 03, 2018 1:31 am
Forum: Higher Secondary Level
Topic: A problem of combinatorics
Replies: 9
Views: 1980

Re: A problem of combinatorics

Mathlomaniac wrote:
Fri Mar 09, 2018 5:49 pm
36×35/2 =630
Read the problem again.