Search found 327 matches

by sm.joty
Sun Apr 01, 2012 2:45 pm
Forum: National Math Camp
Topic: china-1991/1
Replies: 0
Views: 1027

china-1991/1

Find all positive integer $n$ such that $1991$ is the minimum value of $k^2+\left \lfloor \frac{n}{k^2} \right \rfloor$ :D
by sm.joty
Sun Apr 01, 2012 2:40 pm
Forum: National Math Camp
Topic: China-1990-1
Replies: 4
Views: 2123

China-1990-1

Let $a,b$ positive real numbers and $a+b=2$.What is the minimum and maximum value of $\frac{1}{1+a^n}+\frac{1}{1+b^n}$
for any positive integer $n$ :)

Edited
by sm.joty
Sun Apr 01, 2012 2:33 pm
Forum: National Math Camp
Topic: Problem !! Problem !!!
Replies: 3
Views: 1797

Problem !! Problem !!!

If $x,y,z,n \in\mathbb{N}$, and $n\geq z$ then the relation does not hold $x^n+y^n= z^n$ ;)
by sm.joty
Sun Apr 01, 2012 2:25 pm
Forum: National Math Camp
Topic: Theories (Day 1)
Replies: 7
Views: 2758

Re: Theories (Day 1)

Well, Vaia, here's a beginner for you. :roll: Problem: If $d=(a,b)$, then, could we PROVE that there exists integers $s$ and $t$ such that $sa-tb=d$ ? (This is a problem from Adler's Book. Although I know that this is true, I have not been able to prove it :oops: :oops: ) Well, at first assume $m=s...
by sm.joty
Sun Apr 01, 2012 2:15 pm
Forum: National Math Camp
Topic: বুঝি নাই-০২ (BOMC-2)
Replies: 3
Views: 1963

Re: বুঝি নাই-০২ (BOMC-2)

Vaia, The equations of example 1-43 are : $$2x+3y+5z=201;3x+5y+7z=315$$ Multiplying equation-1 by $3$ and equation-2 by $2$ we get : $$6x+9y+15z=603;6x+10y+14z=630$$ Now, subtracting the 1st equation from the 2nd, we get, $$(6x-6x)+(10y-9y)+(14z-15z)=(630-603) \Rightarrow \displaystyle y-z=27$$ Thu...
by sm.joty
Sun Apr 01, 2012 2:11 pm
Forum: National Math Camp
Topic: Theories (Day 1)
Replies: 7
Views: 2758

Re: Theories (Day 1)

sourav das wrote:No question still now :o ? Is there any beginner participating this camp???
I'm not only beginner but also "Moha beginner" :lol:
Now please explain me this. :D
http://www.matholympiad.org.bd/forum/vi ... 9917#p9917
by sm.joty
Sun Apr 01, 2012 9:48 am
Forum: Astronomy & Astrophysics
Topic: Astro Olympiad...........
Replies: 3
Views: 2883

Re: Astro Olympiad...........

Elementary Astor-physics is also a good book and you can download this. just Google now. :D
by sm.joty
Sun Apr 01, 2012 9:40 am
Forum: National Math Camp
Topic: Not so easy (Camp problems) (BOMC-2)
Replies: 6
Views: 2886

Re: Not so easy (Camp problems) (BOMC-2)

may be the only solution for Problem-14 is m=n=1
by sm.joty
Sat Mar 31, 2012 9:23 pm
Forum: National Math Camp
Topic: বুঝি নাই-০২ (BOMC-2)
Replies: 3
Views: 1963

বুঝি নাই-০২ (BOMC-2)

১.আমি এই পোস্টটা অনেক আগে দিসিলাম কিন্তু এখন ও কেউ বুঝায়া দিতে পারল না। :( এখানে একটা নাম্বার থিওরির সমস্যা আছে সেটা কেউ বুঝায়া দাও। http://www.matholympiad.org.bd/forum/viewtopic.php?f=21&t=1775 ২."The Theory Of Number" বইয়ের 1-66 no. উদাহরনটা কেউ বুঝায়া দাও। (মাথার অনেক উপর দিয়া গেসে :cry: ) ...
by sm.joty
Sat Mar 31, 2012 8:55 pm
Forum: National Math Camp
Topic: A Plan
Replies: 15
Views: 4876

Re: A Plan

@Turzo , don't worry to much, it's not so official. When you can get free time, try to see the discussions and try to solve them. If you get stuck, you can tell us. And I think most of us want to work this week. Actually my year final is starting from April 24, and still I have to read a lot. But y...