## Search found 108 matches

Fri Aug 28, 2015 4:44 pm
Forum: National Math Camp
Topic: Exam 2, Online Number Theory Camp, 2015
Replies: 24
Views: 13482

### Re: Exam 2, Online Number Theory Camp, 2015

Should the Vieta Jumping problem be this? If $a|b^2+1$ and $b|a^2+1$, then show that $a^2+b^2+1=3ab$. Here, $a,b$ are both positive. I am not making any assumptions about the problem until Masum vai says so, of course, and neither should anyone else. It wouldn't do to spend your energy solving a pro...
Fri Aug 28, 2015 4:08 pm
Forum: National Math Camp
Topic: Exam 2, Online Number Theory Camp, 2015
Replies: 24
Views: 13482

### Re: Exam 2, Online Number Theory Camp, 2015

Zawadx wrote:ঘাত - কি Power বুঝাচ্ছে?
Yes.
Fri Aug 28, 2015 4:07 pm
Forum: Introductions
Topic: O hai all!
Replies: 3
Views: 4318

### Re: O hai all!

With me as a Marauder, I doubt you will manage your mischiefs before me, but Good Luck all the same.

-Rahul "James" Saha
Wed Aug 26, 2015 11:58 pm
Forum: National Math Camp
Topic: Practice Problemset 2
Replies: 5
Views: 4771

### Re: Practice Problemset 2

Problem 1.6 Hints: Assume $a(a+1)\cdot t(t+1)$ is interesting for some $t$. Now, try to think wishfully-wouldn't it be great if $(a+1)(t+1)$ and $at$ were consecutive integers? Unfortunately, this doesn't work. So, following the same logic, what else can you do? I will admit that I spent most of the...
Mon Aug 24, 2015 11:45 pm
Forum: National Math Camp
Topic: Exam 1, Online Number Theory Camp, 2015
Replies: 15
Views: 10530

### Re: Exam 1, Online Number Theory Camp, 2015

As I haven't attended any online camps before, I am a bit confused about sending solutions. Where do I send them? Do I PM you?
Tue Mar 31, 2015 1:06 pm
Forum: Number Theory
Topic: Disibility by $n!$
Replies: 1
Views: 1407

### Re: Disibility by $n!$

Just some ideas: My idea is that we need to consider every prime factor of $n!$ and show that the exponent of $p$ in $n!$ is less than or equal to its exponent in the product. First of all, the product can be written in a more convenient form: $$A=2^{\frac{n(n-1)}{2}}(2^1-1)\cdots(2^{n-1}-1)$$ This ...
Sun Feb 08, 2015 12:34 pm
Forum: Combinatorics
Topic: Interior regions of a convex $n$ gon
Replies: 3
Views: 5020

### Re: Interior regions of a convex $n$ gon

Every time we draw a new diagonal,it creates one new region,and every time it intersects another previously drawn diagonal,it creates one more region.Hence, Total number of regions if no 3 intersect at a point=number of intersections of two diagonals+number of diagonals You have got a little mistak...
Sat Feb 07, 2015 10:01 pm
Forum: Combinatorics
Topic: Interior regions of a convex $n$ gon
Replies: 3
Views: 5020

### Re: Interior regions of a convex $n$ gon

Every time we draw a new diagonal,it creates one new region,and every time it intersects another previously drawn diagonal,it creates one more region.Hence,

Total number of regions if no 3 intersect at a point=number of intersections of two diagonals+number of diagonals+1