Don't help contest cheaters, please

thaithuan_GC · Poincare Conjecture Offline Joined: 27 Jul 2008 Posts: 192

Sorry, please delete some my posts at
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=221038
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=221668
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=221669
Thanks in advance.

**Posted:** Wed Aug 20, 2008 2:03 am

thaithuan_GC · Poincare Conjecture Offline Joined: 27 Jul 2008 Posts: 192

Another Vietnamese cheater with Physic & Youth Magazine: http://www.artofproblemsolving.com/Forum/search.php?search_author=hoangclub
The member Eldest (M&Y) http://www.artofproblemsolving.com/Forum/viewtopic.php?t=220864
hotboy 12 http://www.artofproblemsolving.com/Forum/viewtopic.php?t=208042&search_id=89410689
pro_math http://www.artofproblemsolving.com/Forum/search.php?search_author=pro_math

**Posted:** Wed Aug 20, 2008 2:15 am

orl

Problems cannot be seen temporarily.

**Posted:** Wed Aug 20, 2008 2:33 am

_________________
Math is like love. A simple idea but it can get complicated.

greenvert

Please delete these topics:
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=221701
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=221697

I suspect that user every is cheater.[/b]

**Posted:** Wed Aug 20, 2008 3:47 am

_________________
4,7,10,12,15,17,20,22,...

blackmouse · P versus NP Offline Joined: 02 Jan 2008 Posts: 21

M&Y-Problems in this issue

T6/275 find all pairs of integer $m$ and $n$ , both greater than $1$ , such that the following equality
$\frac {a^{m + n} + b^{m + n} + c^{m + n}}{m + n} = \frac {a^{m} + b^{m} + c^{m}}{m} = \frac {a^{n} + b^{n} + c^{n}}{n}$
T7/275 Let $k$ be a positive integer and let $a,b,c$ be posiive real numbers such that $abc\le 1$ . Prove that the equality
$\frac {a}{b^k} + \frac {b}{c^k} + \frac {c}{a^k}\ge a + b + c$
T8/275 Let $C$ be a point on a fixed circle whose diameter is $AB = 2R$ ( $C$ is different from $A$ and $B$ ). The incircle of $ABC$ touches $AB$ and $AC$ at $M$ and $N$ , respectively Find the maximum value of the length of $MN$ when $C$ moves on the given fixed circle.

T9/275 Let $(x_n)$ be a sequence such that $x_0$ and $x_{n + 1} = \frac {2x_n + 1}{x_n + 2}$ forall $n = 0,1.2...$

determine $[\sum_{k = 1}^n x_k]$ where $[x]$ denote the lagest integer not exceeding $x$ .

T10/275 Prove that if $a,b,c$ are positive numbers whose product $abc =$ prove that
$\frac {a}{\sqrt {8c^3 + 1}} + \frac {b}{\sqrt {8a^3 + 1}} + \frac {c}{\sqrt {8a^3 + 1}}\ge 1$
T11/275 Let $f: \mathbb R\to\mathbb R$ be a function such that $f(0) = 0$ and $\frac {f(t)}{t}$ is a monotonic function on $\mathbb R/\{0\}$ .Prove that
$xf(y^2 - yz) + yf(z^2 - xy) + zf(x^2 - yz)\ge 0$
T12/275 Let $A_1A_2A_3A_4$ be a tetrahedron. Denote by $B_i,\ i = 1,2,3,4$ the feet of the altitude from a given point $M$ onto $A_iA_{i + 1}$ (where we consider $A_5$ as $A_1$ ). find the smallest value of $\sum_{1\le i\le 4}A_iA_{i + 1}A_iB_i$ .

**Posted:** Wed Sep 17, 2008 1:56 am

April

T6/376. Solve for $x$ :
$\sqrt [3]{x + 6} + \sqrt {x - 1} = x^2 - 1$
T7/376. Let $S$ denote the area of a given triangle $ABC$ , and denote $BC = a$ , $CA = b$ , $AB = c$ . Prove the inequality
$a^2b^2 + b^2c^2 + c^2a^2\ge 16S^2 + \frac {1}{2}\left[a^2(b - c)^2 + b^2(c - a)^2 + c^2(a - b)^2\right]$
When does equality hold?

T8/376. Given a triangle $ABC$ with three sides $BC = a$ , $CA = b$ , $AB = c$ such that $a + c = 2b$ , let $h_a$ , $h_c$ be the altitudes from $A$ and $C$ respectively, and let $r_a$ , $r_c$ denote the $A$ -exradius and $C$ -exradius respectively. Prove that
$\frac {1}{r_a} + \frac {1}{r_c} = \frac {1}{h_a} + \frac {1}{h_c}$
T9/376. The positive real numbers $a$ , $b$ , $c$ , $x$ , $y$ , and $z$ are such that $\begin{cases}cy + bz = a \\ az + cx = b \\ bx + ay = c\end{cases}$
Find the smallest possible value of the expression
$P = \frac {x^2}{1 + x} + \frac {y^2}{1 + y} + \frac {z^2}{1 + z}$
T10/376. Let $f$ be a continuous function on $\mathbb{R}$ such that $f(2010) = 2009$ and $f(x).f_4(x) = 1$ for all $x\in\mathbb{R}$ , where $f_4(x) = f\left(f\left(f\left(f(x)\right)\right)\right)$ . Determine the value of $f(2008)$ .

T11/376. Let $u_1$ , $u_2$ , $\ldots$ , $u_n$ ( $n > 2$ ) be a sequence of positive real numbers such that
i) $\frac {1004}{k} = u_1\ge u_2\ge \ldots\ge u_n$ for some positive integer $k$ .
ii) $u_1 + u_2 + \ldots + u_n = 2008$ .
Show that it is possible to select $k$ elements from the set $(u_n)$ such that in this collection of $k$ numbers, the smallest one is at least half of the largest.

T12/376. Consider the circle $(O)$ and three collinear points $X$ , $Y$ , $H$ that are not on this circle such that $\overline{HX}\cdot\overline{HY}\neq\mathcal{P}_{H/(O)}$ . A straight line $d$ through $H$ meets $(O)$ at two points $M$ and $N$ . $MX$ and $NY$ intersect with $(O)$ again at $P$ and $Q$ respectively. Show that as the line $d$ through $H$ varies, the line connecting $P$ and $Q$ always passes through a fixed point.

**Posted:** Tue Oct 14, 2008 8:53 pm

_________________
"Mathematics, mathematics, mathematics. This much mathematics? No, more!" - Grigore Moisil

No Reason

Could you post the problems of new MYM issue,April?Thanks a lot. Razz

**Posted:** Fri Nov 21, 2008 8:43 am

Allnames

T11/377Consider the sequence $(u_n)(n = 1,2,...)$ given by the following recursive formula
$u_1 = u_2 = 1;u_{n + 1} = 4u_n - 5u_{n - 1}$ for all $n \geq 2$
Prove that $lim_{n \to + infty}(\frac {u_n}{a^n})$ for all real number $a > \sqrt {5}$
T7/377 Let $D$ and $E$ be two points on the side $BC$ of triangle $ABC$ such that $\frac {BD}{CD} = 2\frac {CE}{BE}$
The circumcircle of $ADE$ meets $AB$ and $AC$ at $M$ and $N$ ,respectively.
Prove that regardless of the positions of the points $D$ and $E$ on $BC$ ,the centroid of the triangle $AMN$ lies on a fixed line
T9/377 Determine all trple of real numbers $x;y;z$ such that
$x^6 + y^6 + z^6 - 6(x^4 + y^4 + z^4) + 10(x^2 + y^2 + z^2) - 2(x^3y + y^3z + z^3x) + 6(xy + yz + xz) = 0$
T12/377 Choose three points $A_1,B_1,C_1$ on three sides of a triangle ( $A_1 \in BC;B_1 \in CA;C_1 \in AB$ ) such that $AA_1,BB_1,CC_1$ meet at a common point.Again,choose three points on the sides of triangle ( $A_2 \in B_1C_1;B_2 \in C_1A_1;C_2 \in A_1B_1$ )
Prove that $AA_2,BB_2,CC_2$ meet at a common point if and only if $A_2A_1,B_2B_1,C_2C_1$ so do
T10/377 Find all functions f: $R \to R$ such that
$f(x^3 - y) + 2y(3f^2(x) + y^2) = f(y + f(x))$ for all $x;y \in R$
T6/377 A numbers is said to be a beautiful number if it is a composite number and but it is not a multiple of either $2;3$ or $5$ (for example,the three smallest beautiful numbers are $49,77$ and $91$ )
How many beautiful numbers which are less than $1000$
I cant postt T5 now.sorry Blush

**Posted:** Sat Nov 22, 2008 5:34 pm

Allnames

This issue 378
T6/378 Find the coefficient of $x^2$ in the expansion of
$((...((x - 2)^2 - 2)^2 - ... - 2)^2 - 2)^2$
given that the number $2$ occurs $1004$ times in the expression above and there are $2008$ round brackets
T7/378Find the smallest value of the following expression
$\frac {\sqrt {a_1 + 2008} + \sqrt {a_2 + 2008} + \... + \sqrt {a_n + 2008}}{\sqrt {a_1} + \sqrt {a_2} + ... + \sqrt {a_n}}$
where $n$ is a given positive natural number and $a_1;a_2;...;a_n$ are non-negative real number such that $a_1 + a_2 + ... + a_n = n$
T9/378Does there exist a sequence of positive integers $a_{2003} > a_{2002} > .. > a_2 > a_1$ with $a_{1} = 2003$ such that the folowing two conditions are satisfied:
1)All integers in the interval $(2003;a_{2003})$ are either a member of this sequence or a non-prome
2) $A = \frac {2004}{a_1} + \frac {2004}{a_2} + ... + \frac {2004}{a_{2003}}$ is an integer?
T10/378 Find all continous functions $f,g,h: \mathbb R\rightarrow \mathbb R$ satisfying $f(x + y) = g(x) + h(y)$ for every $x,y\in\mathbb R$
T11/378 Let $H$ and $O$ denote the orthocenter and circumcenter respectively of a triangle $ABC$ .Prove that
$3R - 2OH \leq HA + HB + HC \leq 3R + OH$ where $R$ is its circumradius[/b]

**Posted:** Sat Dec 20, 2008 5:52 am

erudito

http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1368338&sid=b7790eaa7b671168074c9f8f814b8e74#1368338
The user TheHeinrich posted that spiritmarine was a cheater, so please delete this topic and block spiritmarine!!!

**Posted:** Tue Jan 06, 2009 6:43 pm

Potla

Cheating is a common thing not only in this forum, but also in the pre olympiad and other sections. I guess that whenever one sees such a topic identified as the part of a problem magazine or an ongoing contest/competition please report to the moderator to LOCK or DELETE the topic. A few days ago in the Pre Olympiad section I saw a post containing a prob from the CANADIAN MATHS OLYMPIAD and immediately sent a message to the mod........
I have seen this common phenomenon even in other site forums.For the cause of these cheaters people who use their time and solve problems of ongoing contests do not get credited at all, and the cheaters truimph! But I have taken the advice of darij grinberg, so many many thanks...

**Posted:** Sat Jan 10, 2009 12:20 am

MR.129 · Hodge Conjecture Offline Joined: 27 Nov 2008 Posts: 63

problem in this issue this month (january)
For upper secondary schools
T6/379.Let ABC be a triangle Prove the inequality
$\cos A\cos B\cos C \le \frac{1}{8}\cos (B - C)\cos (C - A)\cos (A - B)$
T7/379.Solve for x
$3^x (4^x + 6^x + 9^x ) = 25^x + 2.16^x$
T8/379.Prove that the union of six hemispheres whose diameters are the sides of given tetrahedron must contain the tetrahedron itself

**Posted:** Mon Jan 19, 2009 10:20 pm

darij grinberg

T6/379 is well-known and already discussed here long ago. I wouldn't help new posters with it, but I wouldn't classify everyone who posts it as a cheater.

darij

**Posted:** Wed Jan 21, 2009 5:58 am

_________________
Now the die is cast, the first step taken, a glimmer of hope lights up our lives
Visions of the past, dreams forsaken forming right under our eyes
We are alive...

Allnames

T12 \379 http://www.artofproblemsolving.com/Forum/viewtopic.php?p=1384060#1384060
And warn lhplhp,please

**Posted:** Wed Jan 21, 2009 8:49 pm

Reon · P versus NP Offline Joined: 13 Nov 2008 Posts: 27

Not always do the contest makers invent their own problems ........users may come to know of the problems from a different source.So banning them does not seem right.But there are also contest-cheaters who would intentionally cheat. So I think it is the mods' responsibility to unlock the problems after the contest is over .

**Posted:** Thu Jan 22, 2009 12:41 am

_________________
"Every time you look at the future it changes because you look at it and that changes everything else"
- $The Time Traveler's Guide$

Potla

A new contest cheater:
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=254483
http://www.artofproblemsolving.com/Forum/viewtopic.php?t=254481

Name is N.N. Trung from Vietnam.
Moderators, please warn him.
http://www.artofproblemsolving.com/Forum/search.php?search_author=N.N.Trung

This is N.N. Trung's posts. profile link:
http://www.artofproblemsolving.com/Forum/profile.php?mode=viewprofile&u=55355

**Posted:** Fri Jan 30, 2009 2:49 am

_________________
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N.N.Trung

**Posted:** Fri Jan 30, 2009 5:36 am

Potla

**Posted:** Thu Feb 12, 2009 11:04 pm

_________________
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The Problem Solver's paradise

MR.129 · Hodge Conjecture Offline Joined: 27 Nov 2008 Posts: 63

For uper secondary schools

T6/380.Prove that in any triangle ABC, the following inequality holds:
$\frac{{\cot A.\cot B.\cot C}}{{\sin A.\sin B.\sin C}} \le \left( {\frac{2}{3}} \right)^3$

T7/380.There are 17 ornament betel-nut trees around a circular pond. How many ways are there to chopped pss 4 trees with the condition that no two consecutive trees be removed ?

T8/380.Solve the following system equations with parameter a
$\left\{ \begin{array}{l} 2z(x^2 + a^2 ) = x(x^2 + 9a^2 ) \\ 2y(z^2 + a^2 ) = z(z^2 + 9a^2 ) \\ 2x(y^2 + a^2 ) = y(y...$

**Posted:** Tue Feb 24, 2009 6:55 am

Agr_94_Math · Yang-Mills Theory Offline Joined: 17 Feb 2008 Posts: 707

Well I remeber T6/380 being posted in the pre olympiad section. Well, maybe, it is another well known problem.

**Posted:** Sat Feb 28, 2009 2:50 am