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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.

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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
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D1010 : How it is possible ?
Dattier   3
N 4 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=172840090421781518678763921675392141786000436658021921275090402437796947824966464426797102
59525308036470431210259590181720483369539690621515342820528633073982816814653666658107757108
67856720572225880311472925624694183944650261079955759251769111321319421445397848518597584590
900951222557860592579005088853698315463815905425095325508106272375728975

B=227564340154808184720778276049144229526648735475052708528935496537676518846805227119017278
70644188547893224843051453107076145465733981826429238937805270372241433808862604677609912285
67577953725945090125797351518670892779468968705801340068681556238850340398780828104506916965
606659768601942798676554332768254089685307970609932846902
3 replies
Dattier
Mar 10, 2025
Dattier
4 minutes ago
J
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Number Theory
karasuno   1
N 7 minutes ago by Tkn
Solve the equation $$n!+10^{2014}=m^{4}$$in natural numbers m and n.
1 reply
karasuno
4 hours ago
Tkn
7 minutes ago
J
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Flo0r functi0n
m4thbl3nd3r   5
N 25 minutes ago by pco
Find all positive integers such that $$n=\lfloor \sqrt{n}\rfloor^2+\lfloor \sqrt{n}\rfloor$$
5 replies
m4thbl3nd3r
2 hours ago
pco
25 minutes ago
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Hard T^T
Noname23   1
N 28 minutes ago by RagvaloD
<problem>
1 reply
+1 w
Noname23
an hour ago
RagvaloD
28 minutes ago
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Inequality
jokehim   0
4 hours ago
Problem. Given non-negative real numbers $a,b,c$ satisfying $a+b+c=3.$ Prove that $$\sqrt{a^2+2abc+b^2}+\sqrt{b^2+2abc+c^2}+\sqrt{c^2+2abc+a^2}\le 6.$$Proposed by Phan Ngoc Chau
0 replies
jokehim
4 hours ago
0 replies
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2017 BCSMC Round 2 #3 yellow pig walks on a number line
parmenides51   3
N Today at 4:20 AM by MathPerson12321
A yellow pig walks on a number line starting at $17$. Each step the pig has probability $\frac{8}{17}$ of moving $1$ unit in the positive direction and probability $\frac{9}{17}$ of moving $1$ unit in the negative direction. Find the expected number of steps until the yellow pig visits $0$.
3 replies
parmenides51
Jan 24, 2024
MathPerson12321
Today at 4:20 AM
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number theory
IOQMaspirant   6
N Today at 3:19 AM by Yiyj1
Prove 6|(a + b + c) if and only if 6|(a^3 + b^3 + c^3)
6 replies
IOQMaspirant
Mar 11, 2025
Yiyj1
Today at 3:19 AM
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Mathematica
Wiselady   9
N Today at 3:10 AM by whwlqkd
Let ABC be any triangle. Let side BC pass through point C to point D such that CD=AC. Let P be the second intersection point of the circumscribed circle ACD with the circle with BC as the diameter. Let BP and AC meet at point E and let CP and AB meet at point F. Prove that D, E, F lie on the same straight line.
9 replies
Wiselady
Mar 12, 2025
whwlqkd
Today at 3:10 AM
J
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Collinear proof
Wiselady   1
N Today at 3:01 AM by whwlqkd
Let ABC be any triangle. Let side BC pass through point C to point D such that CD=AC. Let P be the second intersection point of the circumscribed circle ACD with the circle with BC as the diameter. Let BP and AC meet at point E and let CP and AB meet at point F. Prove that D, E, F lie on the same straight line.
IMAGE
1 reply
Wiselady
Today at 1:33 AM
whwlqkd
Today at 3:01 AM
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How to get better at AMC 10
Dream9   2
N Today at 2:01 AM by hashbrown2009
I'm nearly in high school now but only average like 75 on AMC 10 sadly. I want to get better so I'm doing like the first 11 questions of previous AMC 10's almost every day because I also did previous years for AMC 8. Is there any specific way to get better scores and understand more difficult problems past AMC 8? I have almost no trouble with AMC 8 problem given enough time (like 23-24 right with enough time).
2 replies
Dream9
Today at 1:17 AM
hashbrown2009
Today at 2:01 AM
J
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Intermediate Functions
sadas123   3
N Today at 1:30 AM by sadas123
For the set ${a,b,c,d}$, the sum of the products of the elements taken 2 at a time is $ab+ac+ad+bc+bd+cd$; and the sum of the products of the elements taken 3 at a time is $abc+and+acd+bcd$. Let $f(n)$ be the sum of the products of the first 2000 positive integers, taken n at a time. For example, $f(1)$= the sum of the first 2000 positive integers, and $f(2)$ = the sum of the products of the 2000 positive integers, taken two at a time, etc. What is the value of $f(1)$+$f(2)$+$f(3)$+..........+$f(1999)$+$f(2000)$?
3 replies
sadas123
Today at 12:43 AM
sadas123
Today at 1:30 AM
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Stanford Math Tournament PoTW 3/14
stanford-math-tournament   0
Today at 12:34 AM
Stanford Math Tournament is happening in less than a month—register for our online competition here!

Here's this week's SMT Problem of the Week:

Problem

Feel free to reach out to us at stanford.math.tournament@gmail.com with any questions, or ask them in this thread.

Best,

The SMT Team
0 replies
stanford-math-tournament
Today at 12:34 AM
0 replies
J
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Inequality containing arithemetic elements
nhathhuyyp5c   2
N Today at 12:20 AM by kred9
Let $x,y,z$ be positive integers such that $\sqrt{x}+\sqrt{y}+\sqrt{z}=\sqrt{2023}$. Find $\min,\max$ of $\frac{x+y}{z}+\frac{y+z}{x}+\frac{z+x}{y}$
2 replies
nhathhuyyp5c
Yesterday at 3:54 PM
kred9
Today at 12:20 AM
J
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2017 BCSMC Round 2 #10 2^{2^3 x 5^{22}} mod 81
parmenides51   1
N Yesterday at 10:58 PM by CubeAlgo15
Find $2^{2^3 \cdot 5^{22}}$ (mod $81$).
1 reply
parmenides51
Jan 24, 2024
CubeAlgo15
Yesterday at 10:58 PM
J
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J
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limit of sum of a sequence
jasperE3   2
N Apr 13, 2021 by pco
Source: 2001 Moldova MO Grade 11 P7
Set $a_n=\frac{2n}{n^4+3n^2+4},n\in\mathbb N$. Prove that the sequence $S_n=a_1+a_2+\ldots+a_n$ is upperbounded and lowerbounded and find its limit as $n\to\infty$.
2 replies
jasperE3
Apr 13, 2021
pco
Apr 13, 2021
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limit of sum of a sequence
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Source: 2001 Moldova MO Grade 11 P7
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jasperE3
11091 posts
jasperE3
#1 h  Apr 13, 2021, 2:16 AM
Y by
Set $a_n=\frac{2n}{n^4+3n^2+4},n\in\mathbb N$. Prove that the sequence $S_n=a_1+a_2+\ldots+a_n$ is upperbounded and lowerbounded and find its limit as $n\to\infty$.
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jasperE3
11091 posts
jasperE3
#2 h  Apr 13, 2021, 2:19 AM
Y by
The first part is less specific than this.
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pco
23440 posts
pco
#3 h  Apr 13, 2021, 7:11 AM
Y by
jasperE3 wrote:
Set $a_n=\frac{2n}{n^4+3n^2+4},n\in\mathbb N$. Prove that the sequence $S_n=a_1+a_2+\ldots+a_n$ is upperbounded and lowerbounded and find its limit as $n\to\infty$.
Just write $a_n=b_n-b_{n+1}$ where $b_n=\frac 1{n^2-n+2}$

And so $S_n=b_1-b_{n+1}$ and so $\boxed{\lim_{n\to+\infty}S_n=b_1=\frac 12}$
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