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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
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.

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[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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inequality
revol_ufiaw   0
11 minutes ago
Prove that that for any real $x \ge 0$ and natural number $n$,
$$x^n (n+1)^{n+1} \le n^n (x+1)^{n+1}.$$
0 replies
+1 w
revol_ufiaw
11 minutes ago
0 replies
J
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Any nice way to do this?
NamelyOrange   3
N 15 minutes ago by pooh123
Source: Taichung P.S.1 math program tryouts

How many ordered pairs $(a,b,c)\in\mathbb{N}^3$ are there such that $c=ab$ and $1\le a\le b\le c\le60$?
3 replies
NamelyOrange
Apr 2, 2025
pooh123
15 minutes ago
J
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Inequalities
sqing   3
N 16 minutes ago by sqing
Let $ a,b,c> 0 $ and $ \frac{a}{a^2+ab+c}+\frac{b}{b^2+bc+a}+\frac{c}{c^2+ca+b} \geq 1$. Prove that
$$ a+b+c\leq 3 $$
3 replies
+1 w
sqing
Yesterday at 3:52 AM
sqing
16 minutes ago
J
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Inequalities
sqing   0
an hour ago
Let $a,b$ be real numbers such that $ a^2+b^2+a^3 +b^3=4 . $ Prove that
$$a+b \leq 2$$Let $a,b$ be real numbers such that $a+b + a^2+b^2+a^3 +b^3=6 . $ Prove that
$$a+b \leq 2$$
0 replies
sqing
an hour ago
0 replies
J
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that statement is true
pennypc123456789   3
N 2 hours ago by sqing
we have $a^3+b^3 = 2$ and $3(a^4+b^4)+2a^4b^4 \le 8 $ , then we can deduce $a^2+b^2$ \le 2 $ ?
3 replies
pennypc123456789
Mar 23, 2025
sqing
2 hours ago
J
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Distance vs time swimming problem
smalkaram_3549   1
N 2 hours ago by Lankou
How should I approach a problem where we deal with velocities becoming negative and stuff. I know that they both travel 3 Lengths of the pool before meeting a second time.
1 reply
smalkaram_3549
Today at 2:57 AM
Lankou
2 hours ago
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.problem.
Cobedangiu   4
N 3 hours ago by Lankou
Find the integer coefficients after expanding Newton's binomial:
$$(\frac{3}{2}-\frac{2}{3}x^2)^n (n \in Z)$$
4 replies
Cobedangiu
Yesterday at 6:20 AM
Lankou
3 hours ago
J
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inequalities - 5/4
pennypc123456789   2
N 3 hours ago by sqing
Given real numbers $x, y$ satisfying $|x| \le 3, |y| \le 3$. Prove that:
\[ 0 \le (x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) \le 164. \]
2 replies
pennypc123456789
5 hours ago
sqing
3 hours ago
J
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Source of a combinatorics problem
isodynamicappolonius2903   0
Today at 6:47 AM
Does anyone know exactly the source of this problem?? I just remember that it from a combinatorics book of Russia.
0 replies
isodynamicappolonius2903
Today at 6:47 AM
0 replies
J
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KSEA NMSC Mock Contest Group B (Last Problem)
Shiyul   5
N Today at 3:26 AM by Shiyul
Let $a_n$ be a sequence defined by $a_n = a^2 + 1$. Then the product of four consecutive terms in $a_n$ can be written as the product of two terms in $a_n$. Find $p + q$ if $(a_(11))(a_(12))(a_(13))(a_(14)) = (a_p)(a_q)$.
5 replies
Shiyul
Yesterday at 3:09 PM
Shiyul
Today at 3:26 AM
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Regarding IMO prepartion
omega2007   1
N Today at 2:49 AM by omega2007
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compilled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your prespective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
1 reply
omega2007
Yesterday at 3:14 PM
omega2007
Today at 2:49 AM
J
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School Math Problem
math_cool123   6
N Today at 2:37 AM by anduran
Find all ordered pairs of nonzero integers $(a, b)$ that satisfy $$(a^2+b)(a+b^2)=(a-b)^3.$$
6 replies
math_cool123
Apr 2, 2025
anduran
Today at 2:37 AM
J
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New geometry problem
titaniumfalcon   3
N Yesterday at 11:16 PM by mathprodigy2011
Post any solutions you have, with explanation or proof if possible, good luck!
3 replies
titaniumfalcon
Thursday at 10:40 PM
mathprodigy2011
Yesterday at 11:16 PM
J
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Geo Mock #10
Bluesoul   2
N Yesterday at 8:26 PM by Bluesoul
Consider acute $\triangle{ABC}$ with $AB=10$, $AC<BC$ and area $135$. The circle $\omega$ with diameter $AB$ meets $BC$ at $E$. Let the orthocenter of the triangle be $H$, connect $CH$ and extend to meet $\omega$ at $N$ such that $NC>HC$ and $NE$ is the diameter of $\omega$. Draw the circumcircle $\Gamma$ of $\triangle{AHB}$, chord $XY$ of $\Gamma$ is tangent to $\omega$ and it passes through $N$, compute $XY$.
2 replies
Bluesoul
Apr 1, 2025
Bluesoul
Yesterday at 8:26 PM
J
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J
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equiangular inscribed polygon with odd no. of sides is regular (Chile 1991 P2)
parmenides51   0
May 27, 2019
If a polygon inscribed in a circle is equiangular and has an odd number of sides, prove that it is regular.
0 replies
parmenides51
May 27, 2019
0 replies
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equiangular inscribed polygon with odd no. of sides is regular (Chile 1991 P2)
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parmenides51
30629 posts
parmenides51
#1 h  May 27, 2019, 2:49 PM • 2 Y
Y by Adventure10, Mango247
If a polygon inscribed in a circle is equiangular and has an odd number of sides, prove that it is regular.
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