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k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/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.

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0 replies

jlacosta

Apr 2, 2025

0 replies

Concurrency with 10 lines

oVlad 1

Source: Romania EGMO TST 2017 Day 1 P1

Consider five points on a circle. For every three of them, we draw the perpendicular from the centroid of the triangle they determine to the line through the remaining two points. Prove that the ten lines thus formed are concurrent.

1 reply

oVlad

4 hours ago

kokcio

7 minutes ago

Advanced topics in Inequalities

va2010 21

So a while ago, I compiled some tricks on inequalities. You are welcome to post solutions below!

21 replies

va2010

Mar 7, 2015

Novmath

10 minutes ago

GCD of a sequence

oVlad 1

Source: Romania EGMO TST 2017 Day 1 P2

Determine all pairs $(a,b)$ of positive integers with the following property: all of the terms of the sequence $(a^n+b^n+1)_{n\geqslant 1}$ have a greatest common divisor $d>1.$

1 reply

oVlad

4 hours ago

kokcio

17 minutes ago

Test from Côte d'Ivoire Diophantine equation

MENELAUSS 4

determine all triplets $(x;y;z)$ of natural numbers such that
$y \quad \text{is prime }$
$y \quad \text{and} \quad 3 \quad \text{does not divide} \quad z$
$x^3-y^3=z^2$

4 replies

MENELAUSS

Apr 19, 2025

Pal702004

22 minutes ago

College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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College Math Topics in undergraduate and graduate studies

Topics in undergraduate and graduate studies

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k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

0 replies

jlacosta

Apr 2, 2025

0 replies

interesting integral

Martin.s 0

$\int_0^\infty \frac{\sinh(t)}{t \cosh^3(t)} dt$

0 replies

Martin.s

2 hours ago

0 replies

Pre- Calc

AimlessNonsense 1

A rock got stuck in the tread of my tire and when I was driving 45 miles per hour, the rock came loose
and hit the inside of the wheel well of the car. How fast, in miles per hour, was the rock traveling
when it came out of the tread? (The tire has a diameter of 26 inches.)

I have been trying to figure this out for about 3 hours now and I know I am making some small mistake, but cannot seem to figure out what it is.

1 reply

AimlessNonsense

Aug 30, 2015

Mathzeus1024

6 hours ago

How to solve this problem

xiangovo 1

Source: website

How many nonzero points are there on x^3y + y^3z + z^3x = 0 over the finite field \mathbb{F}_{5^{18}} up to scaling?

1 reply

xiangovo

Mar 19, 2025

loup blanc

Today at 11:09 AM

Finite solution for x

Rohit-2006 1

$P(t)$ be a non constant polynomial with real coefficients. Prove that the system of simultaneous equations —
$\int_{0}^{x} P(t)sin t dt =0$ $\int_{0}^{x}P(t) cos t dt=0$ has finitely many solutions $x$ .

1 reply

Rohit-2006

Today at 4:19 AM

Filipjack

Today at 10:41 AM

Featured Content

Problem of the Day 2007 USA Team Selection Test

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Let $\theta$ be an angle in the interval $(0,\pi/2)$ . Given that $\cos \theta$ is irrational, and that $\cos k \theta$ and $\cos[(k + 1)\theta ]$ are both rational for some positive integer $k$ , show that $\theta = \pi/6$ .

N.T.TUAN

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Contest of the Week 1962 Leningrad Math Olympiad

1962 Leningrad Math Olympiad

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1962 Leningrad Math Olympiad

grade 6

6.1 Three people with one double seater motorbike simultaneously headed from city A to city B . How should they act so that time, for which the last of them will get to , was the smallest? Determine this time. Pedestrian speed - 5 km/h, motorcycle speed - 45 km/h, distance from A to B is equal to 60 kilometers .

6.2 / 7.2 The numbers $A$ and $B$ are relatively prime. What common divisors can have the numbers $A+B$ and $A-B$ ?

6.3. A person's age in $1962$ was one more than the sum of digits of the year of his birth. How old is he?

6.4. / 7.3 $15$ magazines lie on the table, completely covering it. Prove that it is possible to remove eight of them so that the remaining magz cover at least $7/15$ of the table area.

6.5. Prove that a $201 \times 201$ chessboard can be bypassed by moving a chess knight, visiting each square exactly once.

6.6. Can an integer whose last two digits are odd be the square of another integer?

PS. You should use hide for answers.Collected here.

parmenides51

view topic

grade 7

7.1. Prove that from the sides of an arbitrary quadrilateral you can fold a trapezoid.

7.2 / 6.2 The numbers $A$ and $B$ are relatively prime. What common divisors can have the numbers $A+B$ and $A-B$ ?

7.3. / 6.4 $15$ magazines lie on the table, completely covering it. Prove that it is possible to remove eight of them so that the remaining magz cover at least $7/15$ of the table area.

7.4 In a six-digit number that is divisible by $7$ , the last digit has been moved to the beginning. Prove that the resulting number is also divisible at $7$ .

7.5* (asterisk problems in separate posts)

7.6 On sides $AB$ and $BC$ of triangle $ABC$ , are constructed squares $ABDE$ and $BCKL$ with centers $O_1$ and $O_2$ . $M_1$ and $M_2$ are midpoints of segments $DL$ and $AC$ . Prove that $O_1M_1O_2M_2$ is a square.

https://cdn.artofproblemsolving.com/attachments/8/1/8aa816a84c5ac9de78b396096cf718063de390.png

PS. You should use hide for answers.Collected here.

parmenides51

view topic

7.5*

The circle is divided into $49$ areas so that no three areas touch at one point. The resulting “map” is colored in three colors so that no two adjacent areas have the same color. The border of two areas is considered to be colored in both colors. Prove that on the circle there are two diametrically opposite points, colored in one color.

parmenides51

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grade 8

8.1 Four circles are placed on planes so that each one touches the other two externally. Prove that the points of tangency lie on one circle.

https://cdn.artofproblemsolving.com/attachments/9/8/883a82fb568954b09a4499a955372e2492dbb8.png

8.2. Let the integers $a$ and $b$ be represented as $x^2-5y^2$ , where $x$ and $y$ are integer numbers. Prove that the number $ab$ can also be presented in this form.

8.3 Solve the equation $x(x + d)(x + 2d)(x + 3d) = a$ .

8.4 / 9.1 Let $a+b+c=1$ , $m+n+p=1$ . Prove that $-1 \le am + bn + cp \le 1$

8.5 Inscribe a triangle with the largest area in a semicircle.

8.6 Three circles of the same radius intersect at one point. Prove that the other three points intersections lie on a circle of the same radius.

https://cdn.artofproblemsolving.com/attachments/4/7/014952f2dcf0349d54b07230e45a42c242a49d.png

8.7 Find the circle of smallest radius that contains a given triangle.

8.8 / 9.2 Given a polynomial $x^{2n} +a_1x^{2n-2} + a_2x^{2n-4} + ... + a_{n-1}x^2 + a_n,$ which is divisible by $x-1$ . Prove that it is divisible by $x^2-1$ .

8.9 Prove that for any prime number $p$ other than $2$ and from $5$ , there is a natural number $k$ such that only ones are involved in the decimal notation of the number $pk$ ..

PS. You should use hide for answers.Collected here.

parmenides51

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k a April Highlights and 2025 AoPS Online Class Information

jlacosta 0

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jlacosta

Apr 2, 2025

0 replies

k Happy Easter!!!

A_Crabby_Crab 37

Happy Easter to all on Aops!!!

I hope everyone on this awesome website will be filled with peace, joy and love this season (its 50 days long y'all so start partying and eat some jelly beans if you can).

37 replies

A_Crabby_Crab

Yesterday at 9:35 AM

MathDolphin95

6 hours ago

Introducing myself at AoPS, and what's your magic wand?

asuth_asuth 934

Hi!

I'm Andrew Sutherland. I'm the new Chief Product Officer at AoPS. As you may have read, Richard is retiring and Ben Kornell and I are working together to lead the company now. I'm leading all the software and digital stuff at AoPS. I just wanted to say hello and introduce myself! I'm really excited to be part of the special community that is AoPS.

Previously, I founded Quizlet as a 15-year-old high school student. I did Course 6 at MIT and then left to lead Quizlet full-time for a total of 14 years. I took a few years off and now I'm doing AoPS! I wrote more about all that on my blog: https://asuth.com/im-joining-aops

I have a question for all of you. If you could wave a magic wand, and change anything about AoPS, what would it be? All suggestions welcome! Thank you.

934 replies

asuth_asuth

Mar 30, 2025

LostInBali

Yesterday at 11:59 PM

k I need help to reset progress in a certain subject but not all subjects

dwead 6

is there a way to reset progress in a certain subject but only that subject so like reset progress in algebra but not in prealgeba?

6 replies

dwead

Apr 19, 2025

mdk2013

Yesterday at 3:00 AM

k Question

jjmmxx 2

"New users are not allowed to post images in the Community."
Can you tell me about this...?

2 replies

jjmmxx

Apr 18, 2025

jjmmxx

Apr 18, 2025

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versus
see for yourself ;)

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China Team Selection Test 2025

2025 EGMO
European Girls MO 2025

2025 Euler Olympiad

2025 Greece National Olympiad
2025 Greece National Olympiad

2025 India National Olympiad
India National Olympiad 2025

2025 India STEMS

2025 International Zhautykov Olympiad
International Zhautykov Olympiad 2025

2025 Iran MO (2nd Round)
National Math Olympiad (Second Round) 2025

2025 Israel National Olympiad (Gillis)
An Olympiad for grades 7-12.

2025 Israel TST

2025 Japan MO Finals
Japan MO Finals 2025

2025 Korea - Final Round
FKMO 2025

2025 Korea Winter Program Practice Test
Korea Winter Program Practice Test 2025

2025 Kyiv City MO Round 1
Problems from first round of Kyiv Mathematical Olympiad 2025

2025 Kyiv City MO Round 2
Problems from second round of Kyiv Mathematical Olympiad 2025

2025 Malaysian APMO Camp Selection Test
Malaysian APMO Camp Selection Test for APMO 2025

2025 Nordic
Nordic 2025

2025 Philippine MO

2025 Poland - First Round

2025 Poland - Second Round
Second Round - Poland 2025

2025 Polish MO Finals
Polish MO Finals 2025

2025 Portugal MO
Portugal MO 2025

2025 Romanian Master of Mathematics
15th RMM 2025

2025 Sharygin Geometry Olympiad
Sharygin Geometry Olympiad 2025

2025 Spain Mathematical Olympiad
Spain Mathematical Olympiad 2025

2025 Taiwan TST Round 1

2025 Taiwan TST Round 2
Taiwan TST Round 2 2025

2025 Turkey EGMO TST
Turkey EGMO TST 2025

2025 Turkey Team Selection Test
Turkey Team Selection Test 2025

2025 Ukraine National Mathematical Olympiad
Ukraine National Mathematical Olympiad 2025

2025 USA IMO Team Selection Test
USA Team Selection Test for IMO 2025

2025 USAJMO
USAJMO 2025

2025 USAMO
USAMO 2025

2025 Vietnam National Olympiad
VMO 2025

2025 Vietnam Team Selection Test
Vietnam Team Selection Test for 2025 IMO

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