ka May Highlights and 2025 AoPS Online Class Information
jlacosta0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.
Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.
Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!
Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.
Introduction to Algebra A
Sunday, May 11 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Wednesday, May 14 - Aug 27
Friday, May 30 - Sep 26
Monday, Jun 2 - Sep 22
Sunday, Jun 15 - Oct 12
Thursday, Jun 26 - Oct 9
Tuesday, Jul 15 - Oct 28
Introduction to Counting & Probability
Thursday, May 15 - Jul 31
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Wednesday, Jul 9 - Sep 24
Sunday, Jul 27 - Oct 19
Introduction to Number Theory
Friday, May 9 - Aug 1
Wednesday, May 21 - Aug 6
Monday, Jun 9 - Aug 25
Sunday, Jun 15 - Sep 14
Tuesday, Jul 15 - Sep 30
Introduction to Algebra B
Tuesday, May 6 - Aug 19
Wednesday, Jun 4 - Sep 17
Sunday, Jun 22 - Oct 19
Friday, Jul 18 - Nov 14
Introduction to Geometry
Sunday, May 11 - Nov 9
Tuesday, May 20 - Oct 28
Monday, Jun 16 - Dec 8
Friday, Jun 20 - Jan 9
Sunday, Jun 29 - Jan 11
Monday, Jul 14 - Jan 19
Paradoxes and Infinity
Mon, Tue, Wed, & Thurs, Jul 14 - Jul 16 (meets every day of the week!)
Intermediate: Grades 8-12
Intermediate Algebra
Sunday, Jun 1 - Nov 23
Tuesday, Jun 10 - Nov 18
Wednesday, Jun 25 - Dec 10
Sunday, Jul 13 - Jan 18
Thursday, Jul 24 - Jan 22
MATHCOUNTS/AMC 8 Basics
Friday, May 23 - Aug 15
Monday, Jun 2 - Aug 18
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
MATHCOUNTS/AMC 8 Advanced
Sunday, May 11 - Aug 10
Tuesday, May 27 - Aug 12
Wednesday, Jun 11 - Aug 27
Sunday, Jun 22 - Sep 21
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Problem Series
Friday, May 9 - Aug 1
Sunday, Jun 1 - Aug 24
Thursday, Jun 12 - Aug 28
Tuesday, Jun 17 - Sep 2
Sunday, Jun 22 - Sep 21 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Monday, Jun 23 - Sep 15
Tues & Thurs, Jul 8 - Aug 14 (meets twice a week!)
AMC 10 Final Fives
Sunday, May 11 - Jun 8
Tuesday, May 27 - Jun 17
Monday, Jun 30 - Jul 21
AMC 12 Problem Series
Tuesday, May 27 - Aug 12
Thursday, Jun 12 - Aug 28
Sunday, Jun 22 - Sep 21
Wednesday, Aug 6 - Oct 22
Introduction to Programming with Python
Thursday, May 22 - Aug 7
Sunday, Jun 15 - Sep 14 (1:00 - 2:30 pm ET/10:00 - 11:30 am PT)
Tuesday, Jun 17 - Sep 2
Monday, Jun 30 - Sep 22
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:
To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.
More specifically:
For new threads:
a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.
Examples: Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿) Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"
b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.
Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".
c) Good problem statement:
Some recent really bad post was:
[quote][/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.
For answers to already existing threads:
d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve , do not answer with " is a solution" only. Either you post any kind of proof or at least something unexpected (like " is the smallest solution). Someone that does not see that is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.
e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.
To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!
Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).
The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
Source: USA Winter TST for IMO 2020, Problem 2, by Merlijn Staps
Two circles and have common external tangents and meeting at . Suppose touches at and touches at . A circle through and intersects again at and again at , such that quadrilateral is convex.
Suppose lines and meet at point , while lines and meet at point . Show that ,, are collinear.
Source: 2025 Vietnam National Olympiad - Problem 3
Let be an acute, scalene triangle with circumcenter , circumcircle , orthocenter . Line meets again at . Let be the midpoint of segments respectively. The line through and perpendicular to meets line at .
a) Line meets again at . Prove that the intersection of line and the perpendicular bisector of lies on the circumcircle of triangle .
b) The line through and perpendicular to meets line at . Line meets again at . Let be the intersection of lines ; be the intersection of lines ; be the intersection of lines . Let be the intersection of lines and be the line through and perpendicular to . Prove that bisects .
Here is another approach that is similar to *p_square*'s idea.
Let r_1, r_2, r_3 be the radii of circles centered near vertices A, B, C, respectively. Let r be the inradius of triangle ABC. Define r_a as the radius of the circle that is tangent to sides AB and AC, and also tangent to a line parallel to BC (but distinct from BC) and to the incircle. Similarly, define r_b and r_c near vertices B and C.
We claim that: because if any of the radii were smaller than these, the circles would not be able to reach and touch the incircle.
Let h_a, h_b, h_c be the altitudes from vertices A, B, C, and let S be the area of triangle ABC. Then we compare the total of the radii to the inradius:
Now we compute the right-hand side:
Recall that the inradius r = \dfrac{2S}{a + b + c}, and also:
Substituting in, we get:
Therefore:
and the proof is complete.
Let be a triangle such that and is obtuse. Point is the circumcenter of triangle , and is the reflection of in . Let be an arbitrary point on line , such that is in between and . Line cuts the circumcircle of in . Circumcircles of triangles and cut in respectively. Prove that is tangent to the circumcircle of triangle .
Let and then we have .obviously the set of prime divisors of and are the same(note that ).(the case is trivial) we'll have two cases:
1-there exist an odd prime such that then prove that (prove this using ).
the rest is solved using inequality.But the other case remaining is:
2-there doesn't exist such :it means that must be .(prove this using again )
I will instead characterize every solution given that and —this is the version of the problem I received.
Clearly works, and by size we require hence no other solution exists for , so assume . Then as a consequence of Zsigmondy there must exist some prime dividing that doesn't divide and thus , unless:
for some , and hence . Then either which is impossible or , which yields and its permutation .
for some , so from which we find that must be a power of , say . Then from which we extract the very ugly answer for all such that .
Since everything is reversible, it follows that the solutions are , and for all such that . (clearly, this implies the original problem)
Assume Then, we have So, we have the solutions Now, assume one of is 1. WLOG let it be Therefore, we have For some prime suppose that such that Then, So, since we have Note that and since So, meaning If then and so Solving, we have If then and meaning Solving, we find no solutions. Now, assume that . Therefore, there exists some prime such that WLOG, let Since we have meaning Since, we must have In conclusion, the solutions are
Observe that and this clearly yields a solution. So assume that Observe that by size
Now, if we get which indeed is a solution as long as
WLOG assume that Then let We get By Zsigmondy's Theorem there is prime dividing but not which is a contradiction, unless we have in which This would give and testing possibilities yields so
To summarize, the solutions are for that yields integer values for the last one.