Search found 217 matches

Mon Oct 14, 2013 6:52 pm
Forum: Geometry
Topic: Where I visualize cyclic ness?
Replies: 4
Views: 2551

Re: Where I visualize cyclic ness?

Sat Apr 27, 2013 11:32 pm
Forum: Geometry
Topic: $AP\perp BC$
Replies: 2
Views: 1580

Re: $AP\perp BC$

Let the touchpoint of the incricle with $BC$ be $F$. As $DP \perp IM$, $IP^2-PM^2=ID^2-DM^2$ And as $EP \perp IN$, $PN^2-PI^2=EN^2-EI^2$ Summing these two, we get $PN^2-PM^2=(EN^2-DM^2)+(ID^2-IE^2)$ $PN^2-PM^2=(EN^2-DM^2)+(IC^2-IB^2)$ [Note that $ID=IC$,$IE=IC$] $PN^2-PM^2=(EN^2-DM^2)+(CF^2-BF^2)$ [...
Sat Apr 27, 2013 9:18 pm
Forum: Geometry
Topic: $AP\perp BC$
Replies: 2
Views: 1580

Re: $AP\perp BC$

This problem is just a mere application of only one lemma.The perpendicular lemma.Use the lemma two times only.
Tue Apr 16, 2013 10:08 pm
Forum: Number Theory
Topic: IMO Preparation Mock 1 Problem 3
Replies: 2
Views: 1595

Re: IMO Preparation Mock 1 Problem 3

না ভাই।করি নাই।করার চেষ্টা করতেছি।করলে দিব সল্যুশান।
Tue Apr 16, 2013 4:28 am
Forum: Number Theory
Topic: Family Of Functions
Replies: 5
Views: 2728

Family Of Functions

Let $n \geq 1$ be an odd integer.Determine all functions $f$ from the set of integers to itself such that for all distinct integers $x$ and $y$,$f(x)-f(y)|x^{n}-y^{n}$.
Mon Apr 15, 2013 7:59 pm
Forum: Number Theory
Topic: IMO Preparation Mock 1 Problem 3
Replies: 2
Views: 1595

IMO Preparation Mock 1 Problem 3

Find all positive integers $m,n \geq 2$,such that,
$1$. $m+1$ is a prime number of the form $4k-1$
$2$.there is a prime number $p$ and non-negative integer $a$,such that
$\frac{m^{2^{n}-1}-1}{m-1}=m^{n}+p^{a}$
Sun Apr 14, 2013 11:26 pm
Forum: Number Theory
Topic: 2002 Czech-Polish-Slovak
Replies: 4
Views: 2292

Re: 2002 Czech-Polish-Slovak

I wish people started posting cool medium level number theory problems like this.
Sat Apr 13, 2013 9:54 pm
Forum: Number Theory
Topic: 2002 Czech-Polish-Slovak
Replies: 4
Views: 2292

2002 Czech-Polish-Slovak

Let $n$ and $p$ be integers such that $n>1$ and $p$ be a prime.If $n|p-1$ and $p|n^3-1$,show that $4p-3$ is a perfect square.
Fri Apr 12, 2013 11:29 pm
Forum: Number Theory
Topic: I Love Mr.Green
Replies: 5
Views: 2276

Re: I Love Mr.Green

My solution is same.
Fri Apr 12, 2013 1:38 am
Forum: Number Theory
Topic: I Love Mr.Green
Replies: 5
Views: 2276

Re: I Love Mr.Green

Well, I meant $a,b \in N_0$. :mrgreen: Sorry for the typo. :mrgreen: I was searching for a title.But i couldn't find anything fitting with this problem.And i don't know the source either.So i gave this title on a whim.Because my forum favourite emo is mrgreen. :mrgreen: :mrgreen: :mrgreen: :mrgreen:...