Search found 26 matches

by sakib.creza
Thu Feb 14, 2013 9:41 am
Forum: Secondary Level
Topic: Geometry Note
Replies: 6
Views: 1394

Re: Geometry Note

Adib Bhai if you have time can you please translate your note in English. Students like me, coming from English medium background find geometry very difficult as our curriculam has very little geometry. And your note is indecipherable for me due to the language barrier.
by sakib.creza
Tue Feb 12, 2013 7:14 pm
Forum: Secondary Level
Topic: Number Theory Proof please
Replies: 1
Views: 694

Number Theory Proof please

If $e=\frac{a}{b}=\frac{c}{d}$, where $b>d$ and $a>c$ prove that $e=\frac{a-c}{b-d}$
I know it is true but have failed to prove it. Can someone pull me out of this misery please?
by sakib.creza
Mon Feb 11, 2013 6:43 am
Forum: Social Lounge
Topic: Help...
Replies: 3
Views: 1343

Re: Help...

1) Geometry Revisited - H.S.M. Coxeter 2) 104 Number Theory Problems - Titu Andreescu, Dorin Andrica, Zuming Feng 3) Elementary Number Theory - Jones and Jones 4) The Art and craft of Problem Solving - Paul Zeitz. P.S. 4) is an all in one book that contains all of Number Theory, Algebra, Calculus. M...
by sakib.creza
Sun Feb 10, 2013 5:00 pm
Forum: Divisional Math Olympiad
Topic: Please Post the Problems of 2013
Replies: 7
Views: 2121

Please Post the Problems of 2013

BDMO is over. Moderators please upload the divisional round questions in the forum.
@Moon Bhai, upload the national round problems formally please.
by sakib.creza
Thu Feb 07, 2013 9:03 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Higher Secondary 2007/7
Replies: 6
Views: 1689

Re: BdMO National Higher Secondary 2007/7

nafistiham wrote: here, $x^7-1=f(x)\cdot(x-1)$
so, \[f(x)|(x^{42}-1),(x^{35}-1),(x^{28}-1),(x^{21}-1),(x^{14}-1),(x^7-1)\]
so, the remainder will be
\[7\]
How does the green line lead to the red line? :? :? :?: :?:
by sakib.creza
Thu Feb 07, 2013 8:59 pm
Forum: National Math Olympiad (BdMO)
Topic: Let us help one another preparing for BdMO national 2013
Replies: 12
Views: 3178

Re: Let us help one another preparing for BdMO national 2013

Shadmanmajid wrote:Problem no.3- For a positive integer n, find the number of solutions of the congruence x
2 ≡ 1 (mod n)
.
What does the portion in red mean??? :? :? :?
by sakib.creza
Thu Feb 07, 2013 7:08 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO 2010 higher secondary Q. 6
Replies: 7
Views: 1785

Re: BdMO 2010 higher secondary Q. 6

$a^2\equiv0^2,1^2,2^2,3^2,4^2\equiv0,1,-1,-1,1 (mod5)$ There are $804$ numbers of form $5n+2$ and $5n+3$ less then $2010$. There are $804$ numbers of form $5n+1$ and $5n+4$ less then $2010$. There are $401$ numbers of form $5n$ less then $2010$. So that number of pair $(a,b)$ be $2.804^2+401^2$. An...
by sakib.creza
Wed Feb 06, 2013 9:39 pm
Forum: Secondary Level
Topic: Help with BDMO Problems
Replies: 1
Views: 803

Re: Help with BDMO Problems

Check this link. Here you will find all the 2012 BDMO Nat. Problems with threads after each problem. You will find your desired solutions once you go to the threads. CLICK: viewtopic.php?f=13&t=1708
by sakib.creza
Wed Feb 06, 2013 7:09 am
Forum: Higher Secondary Level
Topic: Secondary and Higher Secondary Marathon
Replies: 126
Views: 23604

Re: Secondary and Higher Secondary Marathon

Probelm $37$: $\mathbb{N}$ is the set of positive integers and $a\in\mathbb{N}$. We know that for every $n\in\mathbb{N}$, $4(a^n+1)$ is a perfect cube. Prove that $a=1$. Source: Iran NMO-2012-4. Note: In BdMO Summer Camp-2012, a similar problem was given in the Number Theory problem set. Zubaer vai...
by sakib.creza
Tue Feb 05, 2013 9:59 pm
Forum: National Math Olympiad (BdMO)
Topic: BdMO National Secondary 2011/9
Replies: 11
Views: 2956

Re: BdMO National Secondary 2011/9

Can it be generally said that $\sqrt{a}+\sqrt{b}$ and $\sqrt{a}-\sqrt{b}$ is always irrational if both $\sqrt{a}$ and $\sqrt{b}$ are irrational? I think it is because in Secondary and higher Secondary Marathon Adib Bhai had asked for a similar proof which Sanzeed Bhai proved. Also, during the olympi...