Search found 217 matches
- Thu Apr 11, 2013 9:47 pm
- Forum: Number Theory
- Topic: I Love Mr.Green
- Replies: 5
- Views: 4342
I Love Mr.Green
$a,b \in \mathbb N_0$ such that $\forall n \in \mathbb N_0$ ,$2^{n}a+b$ is a perfect square.Prove that $a=0$.
- Thu Apr 11, 2013 3:48 pm
- Forum: Number Theory
- Topic: m and n
- Replies: 4
- Views: 3965
Re: m and n
$2^m-1|2^n-1 \longleftrightarrow m|n$.Let $n=km$. As $2^m-1|\frac{2^n-1}{2^m-1}$
and $2^{m(k-1)}+2^{m(k-2)}+.............+1 \equiv k \equiv 0 (mod 2^m-1)$
\[\Longleftrightarrow 2^m-1|k\]
\[\Longleftrightarrow m(2^m-1)|n\]
and $2^{m(k-1)}+2^{m(k-2)}+.............+1 \equiv k \equiv 0 (mod 2^m-1)$
\[\Longleftrightarrow 2^m-1|k\]
\[\Longleftrightarrow m(2^m-1)|n\]
- Thu Apr 11, 2013 3:04 pm
- Forum: Number Theory
- Topic: Kiran S. Kedlaya
- Replies: 3
- Views: 2952
Kiran S. Kedlaya
Show that if $x$,$y$,$z$ are all positive integers then $(xy+1)(yz+1)(zx+1)$ is a perfect square if and only if $xy+1$,$yz+1$,$zx+1$ are all perfect squares.
- Sun Apr 07, 2013 5:18 pm
- Forum: Number Theory
- Topic: USAMO 2008: Problem 1
- Replies: 2
- Views: 2309
Re: USAMO 2008: Problem 1
$\prod k_i = a^2+a+1$ now we can take $k_n=a^2-a+1$ satisfying $(\prod k_i,k_n)=1$ and $(a^2+a+1)(a^2-a+1) =a^4+a^2+1$
- Sat Apr 06, 2013 2:04 am
- Forum: Algebra
- Topic: N'th power inequality
- Replies: 1
- Views: 2294
Re: N'th power inequality
This is not some problem i came across.It is a generalization of a problem by Mehfuz Zohir Shishir.I posted this on behalf of him.He forgot his forum password.
- Sat Apr 06, 2013 12:52 am
- Forum: Algebra
- Topic: N'th power inequality
- Replies: 1
- Views: 2294
N'th power inequality
All $a_{i}$ are positive real numbers.Prove that,
\[\sum_{cyclic} \frac{1}{a_{i}^{n}+a_{i+1}^{n}+......................+a_{i+n-2}^{n}+a_{1}a_{2}.....a_{n}} \leq \frac{1}{a_{1}a_{2}..........a_{n}}\]
\[\sum_{cyclic} \frac{1}{a_{i}^{n}+a_{i+1}^{n}+......................+a_{i+n-2}^{n}+a_{1}a_{2}.....a_{n}} \leq \frac{1}{a_{1}a_{2}..........a_{n}}\]
- Thu Mar 07, 2013 6:16 pm
- Forum: National Math Camp
- Topic: Cool but may be tough(relatively) (BOMC-2)
- Replies: 4
- Views: 4146
Re: Cool but may be tough(relatively) (BOMC-2)
সত্যি এই ধরনের কমেন্ট দেখলে মেজাজ গরম হয়।SANZEED wrote:I haven't solved it fully yet,but a useful hint:
- Sun Mar 03, 2013 12:58 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: IMO Marathon
- Replies: 184
- Views: 112402
Re: IMO Marathon
Oy Adib,are these primes $p$,$q$ distinct???????
- Sat Mar 02, 2013 3:22 pm
- Forum: Geometry
- Topic: A Very Nice Problem
- Replies: 11
- Views: 7976
Re: A Very Nice Problem
Mahi and Fahim vai, cool avatars.
This is my 200th post.
This is my 200th post.
- Thu Feb 28, 2013 1:48 pm
- Forum: Algebra
- Topic: exponential equation.
- Replies: 4
- Views: 3583
Re: exponential equation.
How could i do this kind of shitty thing?????????? I don't know who gave me the right to turn a curve into a straight line. The first mistake is where i eliminated the square. But the problem is pretty easy.