## Search found 327 matches

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 $k^2+\left \lfloor \frac{n}{k^2} \right \rfloor$
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
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 $x^n+y^n= z^n$
Sun Apr 01, 2012 2:25 pm
Forum: National Math Camp
Topic: Theories (Day 1)
Replies: 7
Views: 2758

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... 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...
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 ? Is there any beginner participating this camp???
I'm not only beginner but also "Moha beginner"
Sun Apr 01, 2012 9:48 am
Forum: Astronomy & Astrophysics
Replies: 3
Views: 2883

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
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: ) ...
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...