Search found 217 matches

by zadid xcalibured
Thu Apr 11, 2013 9:47 pm
Forum: Number Theory
Topic: I Love Mr.Green
Replies: 5
Views: 2190

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 $a=0$. :mrgreen:
by zadid xcalibured
Thu Apr 11, 2013 3:48 pm
Forum: Number Theory
Topic: m and n
Replies: 4
Views: 2594

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 $2^{m(k-1)}+2^{m(k-2)}+.............+1 \equiv k \equiv 0 (mod 2^m-1)$
\[\Longleftrightarrow 2^m-1|k\]
\[\Longleftrightarrow m(2^m-1)|n\]
by zadid xcalibured
Thu Apr 11, 2013 3:04 pm
Forum: Number Theory
Topic: Kiran S. Kedlaya
Replies: 3
Views: 1822

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.
by zadid xcalibured
Sun Apr 07, 2013 5:18 pm
Forum: Number Theory
Topic: USAMO 2008: Problem 1
Replies: 2
Views: 1373

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 $(a^2+a+1)(a^2-a+1) =a^4+a^2+1$
by zadid xcalibured
Sat Apr 06, 2013 2:04 am
Forum: Algebra
Topic: N'th power inequality
Replies: 1
Views: 1284

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.
by zadid xcalibured
Sat Apr 06, 2013 12:52 am
Forum: Algebra
Topic: N'th power inequality
Replies: 1
Views: 1284

N'th power inequality

All $a_{i}$ are positive real numbers.Prove that,
\[\sum_{cyclic} \frac{1}{a_{i}^{n}+a_{i+1}^{n}+......................+a_{i+n-2}^{n}+a_{1}a_{2}.....a_{n}} \leq \frac{1}{a_{1}a_{2}..........a_{n}}\]
by zadid xcalibured
Thu Mar 07, 2013 6:16 pm
Forum: National Math Camp
Topic: Cool but may be tough(relatively) (BOMC-2)
Replies: 4
Views: 2556

Re: Cool but may be tough(relatively) (BOMC-2)

SANZEED wrote:I haven't solved it fully yet,but a useful hint:
If an integer $p$ divides $a$,then find the property of $p$ for this problem.
সত্যি এই ধরনের কমেন্ট দেখলে মেজাজ গরম হয়। :evil:
by zadid xcalibured
Sun Mar 03, 2013 12:58 pm
Forum: International Mathematical Olympiad (IMO)
Topic: IMO Marathon
Replies: 184
Views: 62173

Re: IMO Marathon

Oy Adib,are these primes $p$,$q$ distinct???????
by zadid xcalibured
Sat Mar 02, 2013 3:22 pm
Forum: Geometry
Topic: A Very Nice Problem
Replies: 11
Views: 4806

Re: A Very Nice Problem

Mahi and Fahim vai, cool avatars. :mrgreen:
This is my 200th post. :mrgreen:
by zadid xcalibured
Thu Feb 28, 2013 1:48 pm
Forum: Algebra
Topic: exponential equation.
Replies: 4
Views: 2036

Re: exponential equation.

How could i do this kind of shitty thing?????????? :mrgreen: I don't know who gave me the right to turn a curve into a straight line. :mrgreen: The first mistake is where i eliminated the square. :mrgreen: But the problem is pretty easy. :mrgreen: