and 
Prove that
Y by
find all function F: IR->IR such that 
G
Topic
First Poster
Last Poster
minimum of \sqrt{\frac{a}{b(3a+2)}}+\sqrt{\frac{b}{a(3b+2)}}
parmenides51 11
N
by sqing
Source: JBMO Shortlist 2017 A2
Let 
and 
be positive real numbers such that 
. Find the minimum value of 
and 
be positive real numbers such that 
. Find the minimum value of 
11 replies
IMO Genre Predictions
ohiorizzler1434 14
N
by BR1F1SZ
Everybody, with IMO upcoming, what are you predictions for the problem genres?
Personally I predict:
Personally I predict:
14 replies
Geometry Problem
Euler_Gauss 0
Given that 
is the midpoint of 
, 
bisects 
and intersects 
at 
, 
is the incenter of 
, 
bisects 
and intersects the circumcircle of 
at 
, 
is parallel to and intersects at 
. Prove that 
is the midpoint of 
, 
bisects 
and intersects 
at 
, 
is the incenter of 
, 
bisects 
and intersects the circumcircle of 
at 
, 
is parallel to and intersects at 
. Prove that 
0 replies
Tricky invariant with 3 numbers on the board
Nuran2010 0
Source: Azerbaijan Junior National Olympiad 2021
Initially, the numbers 
written on the board.At every step,Mikail chooses the two numbers 
and substitutes them with 
and 
where 
is the unchosen number on the board. Prove that at least 
negative number must be remained on the board at any step.
written on the board.At every step,Mikail chooses the two numbers 
and substitutes them with 
and 
where 
is the unchosen number on the board. Prove that at least 
negative number must be remained on the board at any step.
0 replies
Inequality with 7th degree root.
Nuran2010 1
N
by sqing
Source: Azerbaijan Junior National Olympiad 2021 P3
For 
positive real numbers,prove the inequality:
![$\sqrt[7]{\frac{a}{b+c}+\frac{b}{a+c}}+\sqrt[7]{\frac{b}{a+c}+\frac{c}{a+b}}+\sqrt[7]{\frac{c}{a+b}+\frac{a}{b+c}} \geq 3$](//latex.artofproblemsolving.com/a/d/4/ad44b49424a2a1891161c4d6bf099e1f6dc63bee.png)
.
positive real numbers,prove the inequality:![$\sqrt[7]{\frac{a}{b+c}+\frac{b}{a+c}}+\sqrt[7]{\frac{b}{a+c}+\frac{c}{a+b}}+\sqrt[7]{\frac{c}{a+b}+\frac{a}{b+c}} \geq 3$](http://latex.artofproblemsolving.com/a/d/4/ad44b49424a2a1891161c4d6bf099e1f6dc63bee.png)
.
1 reply
A coincidence about triangles with common incenter
flower417477 5
N
by mashumaro
have the same incenter .Prove that 
is concyclic iff 
is concurrent
5 replies
Showing a certain number is divisible by 13
BBNoDollar 0
Source: Romanian Mathematical Gazette 2025
Show that 3^(n+2) + 9^(n+1) + 4^(2n+1) + 4^(4n+1) is divisible by 13 for every n natural number.
0 replies
|a^2-b^2-2abc|<2c implies abc EVEN!
tom-nowy 0
Source: Own
Prove that if integers 
and satisfy 
, then 
is an even number.
and satisfy 
, then 
is an even number.
0 replies
interesting function equation (fe) in IR
G
H
G
H
Source: mine
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
or 
The post below has been deleted. Click to close.
This post has been deleted. Click here to see post.
Y by
skellyrah wrote:
find all function F: IR->IR such that
If IR means irrational numbers, and the problem is to find all
such that 
for all 
then setting 
gives a contradictionThis post has been edited 1 time. Last edited by jasperE3, Apr 23, 2025, 9:43 PM
Z
K
Y
N Quick Reply
G
H
