Search found 110 matches
- Mon Aug 15, 2016 6:40 pm
- Forum: Number Theory
- Topic: China TST $2011$ Quiz 3 Day 1
- Replies: 0
- Views: 1992
China TST $2011$ Quiz 3 Day 1
Let $n>1$ be an integer, and let $k$ be the number of distinct prime divisors of $n$. Prove that there exists an integer $a$, $1<a<\frac{n}{k}+1$, such that $n \mid a^2-a$.
- Mon Aug 15, 2016 5:55 pm
- Forum: Geometry
- Topic: China TST $2011$ Day 2
- Replies: 2
- Views: 3011
China TST $2011$ Day 2
Let $H$ be the orthocenter of an acute trangle $ABC$ with circumcircle $\Gamma$. Let $P$ be a point on the arc $BC$ (not containing $A$) of $\Gamma$, and let $M$ be a point on the arc $CA$ (not containing $B$) of $\Gamma$ such that $H$ lies on the segment $PM$. Let $K$ be another point on $\Gamma$ s...
- Mon Aug 15, 2016 5:36 pm
- Forum: Number Theory
- Topic: Sequence of LCM of consecutive integers
- Replies: 1
- Views: 2259
Re: Sequence of LCM of consecutive integers
I will only provide a sketch of part(b) . Note that the problem requires us to prove that for sufficiently large $n$, $f(n)$ is always greater than $N$ . Then it suffices to construct such an $n$. So intuitively, it makes sense that we want to make $n$ as large as possible. My gut reaction after tha...
- Fri Aug 05, 2016 5:37 pm
- Forum: International Mathematical Olympiad (IMO)
- Topic: Problem set collections
- Replies: 0
- Views: 2064
Problem set collections
Hello guys, here is a link to a collection of problem sets that may be useful for training in olympiads. Feel free to share these and post the problems on the forum. We hope you make good use of it.
- Fri Aug 05, 2016 1:46 pm
- Forum: Site Support
- Topic: Visual problems with align code
- Replies: 3
- Views: 10041
Re: Visual problems with align code
Could be a problem with slow internet connections (try using latex in someplace else and see if this is the cause). Also, see if downloading Texfonts (theres a sticky note on this forum) gets rid of this problem.
Also, try using a different browser and see if it works.
Also, try using a different browser and see if it works.
- Fri Aug 05, 2016 11:12 am
- Forum: Algebra
- Topic: Inequality with condition $xy+yz+zx=3xyz$
- Replies: 5
- Views: 8619
Re: Inequality with condition $xy+yz+zx=3xyz$
The thing that always bums me out in ineq probs is the weird constant terms (often +1,-1,+3,-3) . in this prob, its easy to get rid of that; $3 = \frac1x + \frac1y + \frac1z $ . Of course, minus signs never help, so we move these to the left. At this point, you will probably be bothered by the annoy...
- Fri Aug 05, 2016 12:23 am
- Forum: Geometry
- Topic: Iran TST Incircle configuration
- Replies: 1
- Views: 2285
Iran TST Incircle configuration
Let $ABC$ be a triangle with incenter $I$ and contact
triangle $DEF$. Let $M$ be the foot of the perpendicular from $D$ to $EF$ and let $P$ be the
midpoint of $DM$. If $H$ is the orthocenter of triangle $BIC$, prove that $PH$ bisects $EF$.
triangle $DEF$. Let $M$ be the foot of the perpendicular from $D$ to $EF$ and let $P$ be the
midpoint of $DM$. If $H$ is the orthocenter of triangle $BIC$, prove that $PH$ bisects $EF$.
- Thu Aug 04, 2016 11:46 pm
- Forum: Social Lounge
- Topic: Chat thread
- Replies: 53
- Views: 82585
Re: Chat thread
I am Rahul Saha, from Dhaka. My interests include topics like social equity, songs, tv shows, movies and whatnot.
- Thu Aug 04, 2016 11:43 pm
- Forum: Social Lounge
- Topic: Chat thread
- Replies: 53
- Views: 82585
Re: Chat thread
And the wall will be SO good, people - I kid you not - it will keep the bashers out- we wont even have to deport them anymore .Zawadx wrote:#make_BdMO_forum_great_again
We're gonna make a wall, and we'll get the bashers to pay for it!
- Thu Aug 04, 2016 4:28 pm
- Forum: Geometry
- Topic: Cyclic intersections of $AH$ and $BO$ gives similar $\Delta$
- Replies: 2
- Views: 2832
Cyclic intersections of $AH$ and $BO$ gives similar $\Delta$
In $\triangle ABC$, let $H$ and $O$ be the orthocentre and circumcentre respectively. Now, let $X=AH\cap BO,Y=BH\cap CO, Z=CH\cap AO$. Now, prove that, $\triangle ABC$ and $\triangle XYZ$ are similar.