[/quote]
,
for which 
is the square of an integer
of natural numbers with 
of 
if the product of the elements of 
![\[\sum_{i=1}^n \sum_{j=1}^n \left\lfloor \frac{ij}{n+1} \right\rfloor=\frac{n^2(n-1)}{4}\]](http://latex.artofproblemsolving.com/e/7/f/e7fb8c20a43535b5aaed5ab254f1ef043263c62b.png)
true?
be an integer greater than zero. Then, the value of the sum of the reciprocals of the cubes of the roots of the equation![\[
mx^4 + 8x^3 - 139x^2 - 18x + 9 = 0
\]](http://latex.artofproblemsolving.com/a/3/a/a3a9bca412e927632e4921c51f2a6593409031d9.png)
is equal to:
for which there exists an even natural number 
such that the number![\[
(a - 1)(a^2 - 1)\cdots(a^n - 1)
\]](http://latex.artofproblemsolving.com/9/c/a/9caf4eeb82ff46b5ba55ab4b6bc28f0cace586ec.png)
is a perfect square.
and 
be on segment 
of an acute triangle 
such that 
and 
.
be the points on 
and 
,
and 
.
and 
is on the circumference of triangle 
,![\[
\sum_{\text{cyc}} \sqrt{1 + \left(x\sqrt{1 + y^2} + y\sqrt{1 + x^2}\right)^2} \geq \sum_{\text{cyc}} xy + 2\sum_{\text{cyc}} x
\]](http://latex.artofproblemsolving.com/9/5/5/955863a0cf8747ae45b736b0631f243d3908eb84.png)
be triangle, inscribed in parabola. Tangents in points 
forms triangle 
.
)
such that the equality 
holds for all pairs of real numbers 
.
is an obvious solution. Now, let 
.
or 
.
.
Y by mainstain, Sippi
This will be the last semicolon math contest, at least for a while. Farewell, for now!
Hello AoPS!
One month ago, I ran semicolon math round 2, and today I am happy to host the final contest! Semicolon Math is a platform that offers math contests with 2 easy, 2 medium, and 2 hard AIME level problems. The format is similar to contests you will find on some competitive programming contests.
Create an account on https://scmath.herokuapp.com and view our contest here: https://scmath.herokuapp.com/contests/!
Conclusion
Sorry for the late conclusion post.
Thanks for everyone who participated in the contests!
Best,
mathmastersd
Credits
Thanks to hurdler, miguel00, and myself (mathmastersd) for proposing problems or giving feedback! Your help has made this contest possible!
Clarification
Sorry for the inconvenience but it has come to my attention that the last problem in the contest has an error. So everyone will be receiving free points for this problem.
Format of this contest
Scoring
Join our discord server and chat!
The purpose of this Semicolon Math server is create a friendly atmosphere and environment for problem solvers. This server can be used to interact with other interested math students and discuss the contest problems AFTER the testing window closes. You do not need to be a current or previous competitor to be here. Thanks, have fun, and enjoy your stay.
The link to the Discord server is available in the about section of our website!
Rules (please read!)
The most up to date rules are available here.
That's it!
Thank you so much and I hope you have fun in this contest! Once again:
Create an account on https://scmath.herokuapp.com and view our contest here: https://scmath.herokuapp.com/contests/!
Best,
mathmastersd
Hello AoPS!
One month ago, I ran semicolon math round 2, and today I am happy to host the final contest! Semicolon Math is a platform that offers math contests with 2 easy, 2 medium, and 2 hard AIME level problems. The format is similar to contests you will find on some competitive programming contests.
Create an account on https://scmath.herokuapp.com and view our contest here: https://scmath.herokuapp.com/contests/!
Conclusion
Sorry for the late conclusion post.
- Join our discord server, if you are interested in chatting. Link is on the about section of our website.
- Scoreboard: available here
- Problems plus partial solutions: available here
- Collection of all our contests: available here
Thanks for everyone who participated in the contests!
Best,
mathmastersd
Credits
Thanks to hurdler, miguel00, and myself (mathmastersd) for proposing problems or giving feedback! Your help has made this contest possible!
Clarification
Sorry for the inconvenience but it has come to my attention that the last problem in the contest has an error. So everyone will be receiving free points for this problem.
Format of this contest
- 6 problems
- 2 hours to solve them
- 2 easy AIME-like problems (difficulty problems 1-5), 2 medium AIME-like problems (difficulty of problems 6-10), 2 hard AIME-like problems (difficulty of problems 11-15)
- Choose a 2 hour interval between July 29, 2022, 6:00 p.m. (UTC) and August 5, 2022, 8:00 p.m. (UTC) to participate (convenient!) The contest will end at August 5, 2022, 8:00 p.m. (UTC) for everyone, so plan ahead to get a full one hour interval!
- Users get instant feedback after submitting a problem
- Problems can have any integer values (including negative ones)
- You can make AT MOST 5 submissions per problem in a contest. Also, keep in mind if you submit the same answer twice, it will count as two submissions, so be organized in your work!
Scoring
- For this contest, the point value for the problems is
- Users cannot view the contest scoreboard until the contest ends for everyone
- The contest scoreboard is ranked by total points from problems solved, and then total penalty from all the problems
- The penalty of one problem is computed as:
time problem gets solved in minutes + 10 × (number of wrong submissions)
Join our discord server and chat!
The purpose of this Semicolon Math server is create a friendly atmosphere and environment for problem solvers. This server can be used to interact with other interested math students and discuss the contest problems AFTER the testing window closes. You do not need to be a current or previous competitor to be here. Thanks, have fun, and enjoy your stay.
The link to the Discord server is available in the about section of our website!
Rules (please read!)
The most up to date rules are available here.
- You CAN ONLY use scratch paper, pencils, erasers, colored pencils/pens/markers, rulers, and compasses
- You CANNOT use protractors or graph paper
- You CANNOT use any calculator (online or offline) or any computing services (like WolframAlpha). You also cannot write any code to solve the problems. All problems must be solved by YOU and not a computer.
- You CANNOT discuss the problems with any other person when the contest is RUNNING. ONLY SOLVE THE PROBLEMS BY YOURSELF.
- You can make AT MOST 5 submissions per problem in a contest. Also, keep in mind if you submit the same answer twice, it will count as two submissions, so be organized in your work!
- You can only use ONE account to participate in contests. Alt accounts are NOT ALLOWED.
- If you have a technical issue DURING the contest that is within our control (e.g. the server goes down but your wifi works fine), please DM mathmastersd on Discord (using our server). DO NOT ASK PUBLICLY ON THE SERVER. Also, DO NOT ask how to solve a problem, the answer to a problem, or anything regarding the problems. If a problem is unclear, please move on and try it later.
- All technical issues will be posted on our Discord server. Any problem fixes will be posted AFTER the contest ends for everyone. The fixes are available directly in the problem statements.
- Tip: After submitting an answer, please wait at least 15 seconds for the website to load and return your verdict. DO NOT refresh the page.
- If you are a current staff or former member (i.e. you joined staff in the past), you CANNOT participate in ANY rounds.
- Failure to follow the rules MAY result in your account getting DELETED.
That's it!
Thank you so much and I hope you have fun in this contest! Once again:
Create an account on https://scmath.herokuapp.com and view our contest here: https://scmath.herokuapp.com/contests/!
Best,
mathmastersd
This post has been edited 3 times. Last edited by mathmastersd, Aug 6, 2022, 12:09 AM
