Three 3-digit numbers

by miiirz30, Mar 31, 2025, 5:38 PM

Leonard wrote three 3-digit numbers on the board whose sum is $1000$ . All of the nine digits are different. Determine which digit does not appear on the board.

Proposed by Giorgi Arabidze, Georgia

algebra

Euler Olympiad

Polynomial optimization problem

by ReticulatedPython, Mar 31, 2025, 2:51 PM

Let $p(x)=-ax^4+x^3$ , where $a$ is a real number. Prove that for all positive $a$ , $p(x) \le \frac{27}{256a^3}.$

This post has been edited 1 time. Last edited by ReticulatedPython, Mar 31, 2025, 3:03 PM

algebra

polynomial

functional equation

by Tony_stark0094, Mar 31, 2025, 1:29 PM

solve for $f:R \rightarrow R$ such that
$f(x+f(y))=y+f(x+1)$

functional equation

algebra

View Comments (4)

Inequality

by lgx57, Mar 31, 2025, 1:24 PM

Let $x,y,z \ge 0$ and $xyz=1$ . Prove that

$\sum \frac{1}{x^2+x+1} \ge 1$

algebra

inequalities

Solve the equetion

by yt12, Mar 31, 2025, 8:34 AM

Solve the equetion: $\sin 2x+\tan x=2$

f(x^2-1998x)-f^2(2x-1999)>=1/4 (VI Soros Olympiad 1990-00 R1 9.4)

by parmenides51, May 27, 2024, 8:18 PM

Is there a function $f(x)$ , which satisfies both of the following conditions:

a) if $x \ne y$ , then $f(x)\ne f(y)$

b) for all real $x$ , holds the inequality $f(x^2-1998x)-f^2(2x-1999)\ge \frac14$ ?

This post has been edited 1 time. Last edited by parmenides51, May 27, 2024, 8:43 PM

algebra

functional

functional inequation

inequalities

Inequalities (Please help me!!!)

by yt12, Mar 4, 2023, 2:45 PM

Let $a,b,c$ be reals with $a+b+c=1$ and $a,b,c \ge \frac{-3}{ 4}$ . Prove that
$\frac{a}{a^2+1}+\frac{b}{b^2+1}+\frac{c}{ c^2+1} \le \frac{9}{ 10}$

inequalities

algebra

IMO

Easiest functional equation?

by ZETA_in_olympiad, Mar 19, 2022, 3:20 PM

Here I want the users to post the functional equations that they think are the easiest. Everyone (including the one who posted the problem) are able to post solutions.

This post has been edited 1 time. Last edited by ZETA_in_olympiad, Mar 19, 2022, 3:31 PM
Reason: Making the equation plural

Functional Equations

algebra

functional equation

functional equation in R2

by jasperE3, Mar 27, 2021, 10:18 PM

Find all functions $f:\mathbb R\times\mathbb R\to\mathbb R$ such that:
$a)\enspace f(x+z,y+z)=f(x,y)+z$
$b)\enspace f(xw,yw)=wf(x,y)$
both hold $\forall w,x,y,z\in\mathbb R,w\ne0$ .

This post has been edited 1 time. Last edited by jasperE3, Mar 27, 2021, 10:20 PM

algebra

functional equation

function

Functional Equation

by ab_xy123, Mar 16, 2020, 1:08 PM

Find all solutions to the functional equation $f(1-x) = f(x) + 1 - 2x$

algebra

functional equation

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Submit

The most viewed blog of all time
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wow this blog is ancient
it started when I was an infant
wow and like 1.5 million views
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no ur cool

tbh it scares me too I still dont know where those views came from
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wowwww this blog is so cool
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it scares me how many views this blog has
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bruh
this blog started when i was like 2 months old
by TimmyL, Sep 27, 2024, 9:18 AM
1579363 visits rn, curious how many views (if any) this blog gets now
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interesting lol
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EpicSkills32 reaped on Jul 27, 18:44:19 and gained 10 minutes, 57 seconds

orz orz orz

highest raw of the game so far
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whoa this blog is old
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greetings
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hi $\text{[math]}$
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orzorzorz can i have contrib
by dbnl, Aug 11, 2023, 10:18 PM
1.5M views pro
by Turtle09, Sep 26, 2022, 12:11 PM
orz how did i not know about u before
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wow, this css is SOOOOOO annoying!
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What is this i don't even..
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Dang What 's wit hthe spinning transitions???
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cani be contriB?
I'll add you

BTW, lets talk about the NBA playoffs 2012
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ur css is intersting
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This CSS is really cool! How did you do it??
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what!?
nav bar is not spinning
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contrib please?
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Why is the blog spinning? I have never encountered this in my life. Sure makes typing difficult..
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ok electric
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MY BLOG IS MORE BORING
ALONG WITH OCCASIONAL MISUSE OF CAPS
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contrib???
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by EpicSkills32, May 2, 2012, 5:22 AM
by EpicSkills32, Apr 26, 2012, 5:11 PM

536 shouts

Seems

by miiirz30, Mar 31, 2025, 5:38 PM

by ReticulatedPython, Mar 31, 2025, 2:51 PM

by Tony_stark0094, Mar 31, 2025, 1:29 PM

by lgx57, Mar 31, 2025, 1:24 PM

by yt12, Mar 31, 2025, 8:34 AM

by parmenides51, May 27, 2024, 8:18 PM

by yt12, Mar 4, 2023, 2:45 PM

by ZETA_in_olympiad, Mar 19, 2022, 3:20 PM

by jasperE3, Mar 27, 2021, 10:18 PM

by ab_xy123, Mar 16, 2020, 1:08 PM