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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
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.

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[*]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]
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0 replies
jlacosta
May 1, 2025
0 replies
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Logarithmic function
jonny   1
N 16 minutes ago by Mathzeus1024
If $\log_{6}(15) = a$ and $\log_{12}(18)=b,$ Then $\log_{25}(24)$ in terms of $a$ and $b$
1 reply
jonny
Jul 15, 2016
Mathzeus1024
16 minutes ago
J
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Function equation
hoangdinhnhatlqdqt   1
N an hour ago by Mathzeus1024
Find all functions $f:\mathbb{R}\geq 0\rightarrow \mathbb{R}\geq 0$ satisfying:
$f(f(x)-x)=2x\forall x\geq 0$
1 reply
hoangdinhnhatlqdqt
Dec 17, 2017
Mathzeus1024
an hour ago
J
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Inequality with function.
vickyricky   3
N an hour ago by SpeedCuber7
If x satisfies the inequalit$ |x - 1| + |x - 2| + |x - 3| \ge 6$, then
$(a) 0 \le x \le 4. (b) x \le 0 or x \ge 4. (c) x \le -2 or x \ge 4$. (d) None of these.
3 replies
1 viewing
vickyricky
May 28, 2018
SpeedCuber7
an hour ago
J
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Writing/Evaluating Exponential Functions
Samarthsshah   1
N an hour ago by Mathzeus1024
Rewrite the function and determine if the function represents exponential growth or decay. Identify the percent rate of change.

y=2(9)^-x/2
1 reply
Samarthsshah
Jan 30, 2018
Mathzeus1024
an hour ago
J
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D1028 : A strange result about linear algebra
Dattier   2
N 4 hours ago by ysharifi
Source: les dattes à Dattier
Let $p>3$ a prime number, with $H \subset M_p(\mathbb R), \dim(H)\geq 2$ and $H-\{0\} \subset GL_p(\mathbb R)$, $H$ vector space.

Is it true that $H-\{0\}$ is a group?
2 replies
Dattier
Yesterday at 1:49 PM
ysharifi
4 hours ago
J
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Mathematical expectation 1
Tricky123   0
5 hours ago
X is continuous random variable having spectrum
$(-\infty,\infty) $ and the distribution function is $F(x)$ then
$E(X)=\int_{0}^{\infty}(1-F(x)-F(-x))dx$ and find the expression of $V(x)$

Ans:- $V(x)=\int_{0}^{\infty}(2x(1-F(x)+F(-x))dx-m^{2}$

How to solve help me
0 replies
Tricky123
5 hours ago
0 replies
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Double integrals
fermion13pi   1
N Today at 8:11 AM by Svyatoslav
Source: Apostol, vol 2
Evaluate the double integral by converting to polar coordinates:

\[ \int_0^1 \int_{x^2}^x (x^2 + y^2)^{-1/2} \, dy \, dx \]
Change the order of integration and then convert to polar coordinates.

1 reply
fermion13pi
Yesterday at 1:58 PM
Svyatoslav
Today at 8:11 AM
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Roots of a polynomial not in the disc of unity
Fatoushima   1
N Today at 7:59 AM by alexheinis
Show that the polynomial $p_n(z)=\sum_{k=1}^nkz^{n-k}$ has no roots in the disc of unity.
1 reply
Fatoushima
Today at 1:48 AM
alexheinis
Today at 7:59 AM
J
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Integration Bee Kaizo
Calcul8er   61
N Today at 6:36 AM by Svyatoslav
Hey integration fans. I decided to collate some of my favourite and most evil integrals I've written into one big integration bee problem set. I've been entering integration bees since 2017 and I've been really getting hands on with the writing side of things over the last couple of years. I hope you'll enjoy!
61 replies
Calcul8er
Mar 2, 2025
Svyatoslav
Today at 6:36 AM
J
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Japanese Olympiad
parkjungmin   2
N Today at 5:26 AM by parkjungmin
It's about the Japanese Olympiad

I can't solve it no matter how much I think about it.

If there are people who are good at math

Please help me.
2 replies
parkjungmin
Yesterday at 6:51 PM
parkjungmin
Today at 5:26 AM
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Japanese high school Olympiad.
parkjungmin   0
Today at 5:25 AM
It's about the Japanese high school Olympiad.

If there are any students who are good at math, try solving it.
0 replies
parkjungmin
Today at 5:25 AM
0 replies
J
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Marginal Profit
NC4723   2
N Today at 4:35 AM by Juno_34
Please help me solve this
2 replies
NC4723
Dec 11, 2015
Juno_34
Today at 4:35 AM
J
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D1029 : A story of equivalent and increasing sequence
Dattier   1
N Yesterday at 8:13 PM by Phorphyrion
Source: les dattes à Dattier
Let $(a_n) \in (\mathbb R^*_+) ^\mathbb N$ an increasing sequence, with $\forall (b_n) \in (\mathbb R^*_+) ^\mathbb N$, if $\lim \dfrac {a_n}{b_n}=1$ then $(b_n)$ increasing, from a certain rank.

Is it true $\exists M >1, \exists N \in \mathbb N, \forall n>N, \dfrac {a_{n+1}}{a_n} \geq M$ ?
1 reply
Dattier
Yesterday at 5:47 PM
Phorphyrion
Yesterday at 8:13 PM
J
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Hello, I'm a math Olympiad question for a Japanese high school. I'm asking here
parkjungmin   0
Yesterday at 6:41 PM
This is very difficult, can anyone solve it?

The percentage of correct answers is low
0 replies
parkjungmin
Yesterday at 6:41 PM
0 replies
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hard number theory
eric201291   2
N Apr 18, 2025 by eric201291
Prove:There are no integers x, y, that y^2+9998587980=x^3.
2 replies
eric201291
Apr 16, 2025
eric201291
Apr 18, 2025
J
hard number theory
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Reveal topic tags
number theory
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eric201291
208 posts
eric201291
#1 h  Apr 16, 2025, 2:17 PM
Y by
Prove:There are no integers x, y, that y^2+9998587980=x^3.
Z K Y
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Kempu33334
609 posts
Kempu33334
#2 h  Apr 17, 2025, 12:50 AM
Y by
This is a Mordell curve, however I don't know how to prove that this doesn't have any solutions. Perhaps such kind of modulo or manipulation (I can't find one)?
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eric201291
208 posts
eric201291
#3 h  Apr 18, 2025, 9:22 AM
Y by
Let me tell you sth:9998587980=2154^3+2154^2, and this thing is very important, so...
y^2+2154^2=x^3-2154^3, so by (-1/p) when p=4k+3 is -1, so done!
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