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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
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[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
J
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Help meee
hanzo.ei   1
N 15 minutes ago by Curious_Droid
Given a triangle ABC with (O) and (I) as its circumcircle and incircle, respectively. The incircle (I) touches BC, CA, AB at D, E, F, respectively. Prove that OI passes through the centroid of triangle DEF.
1 reply
hanzo.ei
25 minutes ago
Curious_Droid
15 minutes ago
J
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D1010 : How it is possible ?
Dattier   10
N 19 minutes ago by Dattier
Source: les dattes à Dattier
Is it true that$$\forall n \in \mathbb N^*, (24^n \times B \mod A) \mod 2 = 0 $$?

A=1728400904217815186787639216753921417860004366580219212750904
024377969478249664644267971025952530803647043121025959018172048
336953969062151534282052863307398281681465366665810775710867856
720572225880311472925624694183944650261079955759251769111321319
421445397848518597584590900951222557860592579005088853698315463
815905425095325508106272375728975

B=2275643401548081847207782760491442295266487354750527085289354
965376765188468052271190172787064418854789322484305145310707614
546573398182642923893780527037224143380886260467760991228567577
953725945090125797351518670892779468968705801340068681556238850
340398780828104506916965606659768601942798676554332768254089685
307970609932846902
10 replies
+1 w
Dattier
Mar 10, 2025
Dattier
19 minutes ago
J
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Squares on harmonic quadrilateral
Tkn   2
N 19 minutes ago by Curious_Droid
Let $ABCD$ be a cyclic quadrilateral for which $AB\cdot CD=AD\cdot BC$. Construct two squares $BCEF$ and $DCGH$ externally on the sides $\overline{BC}$ and $\overline{DC}$ respectively.
Suppose that $\overleftrightarrow{BD}$ meets $\overleftrightarrow{AC}$ at $X$, $\overleftrightarrow{BE}$ meets $\overleftrightarrow{DG}$ at $Z$ and $O$ denotes circumcenter of $ABCD$. Prove that $(ZEG)$ and $(ZBD)$ meets again on $\overleftrightarrow{OX}$.
2 replies
Tkn
5 hours ago
Curious_Droid
19 minutes ago
J
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D1014 : Intersection of set
Dattier   1
N 29 minutes ago by Dattier
Source: les dattes à Dattier
Let $A=\{1,...,n\}$ with $\forall i\in A,B_i \subset A$ and $\forall i \in A, \text{card}(\bigcap \limits_{k=1,k\neq i}^n B_k)\geq 2$.

Is it true that $\bigcap \limits_{k=1}^n B_k \neq \emptyset$?
1 reply
Dattier
Yesterday at 12:33 PM
Dattier
29 minutes ago
J
No more topics!
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J
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gcd of binomial (2n, 2i+1) from 0<=i<i+1
parmenides51   2
N Sep 17, 2018 by GorgonMathDota
Source: SRMC 2012
Let $n > 1$ be an integer.
Determine the greatest common divisor of the set of numbers $\left\{ \left( \begin{matrix} 2n \\ 2i+1 \\ \end{matrix} \right):0 \le i \le n-1 \right\}$
i.e. the largest positive integer, dividing $\left( \begin{matrix} 2n \\ 2i+1 \\ \end{matrix} \right)$ without remainder for every $i = 0, 1, ..., n–1$ .
(Here $\left( \begin{matrix} m \\ l \\ \end{matrix} \right)=\text{C}_{m}^{l}=\frac{m\text{!}}{l\text{!}\left( m-l \right)\text{!}}$ is binomial coefficient.)
2 replies
parmenides51
Sep 3, 2018
GorgonMathDota
Sep 17, 2018
J
gcd of binomial (2n, 2i+1) from 0<=i<i+1
G H J
Reveal topic tags
number theory
greatest common divisor
binomial coefficients
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Source: SRMC 2012
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parmenides51
30627 posts
parmenides51
#1 h  Sep 3, 2018, 3:10 PM • 2 Y
Y by Adventure10, Mango247
Let $n > 1$ be an integer.
Determine the greatest common divisor of the set of numbers $\left\{ \left( \begin{matrix} 2n \\ 2i+1 \\ \end{matrix} \right):0 \le i \le n-1 \right\}$
i.e. the largest positive integer, dividing $\left( \begin{matrix} 2n \\ 2i+1 \\ \end{matrix} \right)$ without remainder for every $i = 0, 1, ..., n–1$ .
(Here $\left( \begin{matrix} m \\ l \\ \end{matrix} \right)=\text{C}_{m}^{l}=\frac{m\text{!}}{l\text{!}\left( m-l \right)\text{!}}$ is binomial coefficient.)
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Eray
381 posts
Eray
#2 h  Sep 3, 2018, 3:18 PM • 2 Y
Y by Adventure10, Mango247
See here.
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GorgonMathDota
1063 posts
GorgonMathDota
#3 h  Sep 17, 2018, 1:23 AM • 2 Y
Y by Adventure10, Mango247
Is it basically the same since this ranges over odd numbers not for all natural numbers?
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