by Fly_into_the_sky, May 31, 2025, 5:15 PM 
and i am willing to be able to do P1/P4 combos (or even more)
by JARP091, May 31, 2025, 4:10 PM ![\[
\text{Find all functions } f : \mathbb{R} \to \mathbb{R} \text{ such that:} \\
f(a^4 + a^2b^2 + b^4) = f\left((a^2 - f(ab) + b^2)(a^2 + f(ab) + b^2)\right)
\]](http://latex.artofproblemsolving.com/2/a/7/2a73a5e58eab4a994fbd83160fb79a0b00152951.png)
by Royal_mhyasd, May 30, 2025, 6:10 PM by RainbowNeos, May 29, 2025, 1:03 PM 
that, for all 
and positive real numbers 
, there is![\[\sum_{i=1}^n \frac{x_i^2}{\sum_{j=1}^i x_j}\geq C \ln n\left(\prod_{i=1}^n x_i\right)^{\frac{1}{n}}\]](http://latex.artofproblemsolving.com/4/8/b/48b9fc4af5a20de7fd9dfc45a74d5aa27e615e46.png)
by OgnjenTesic, May 22, 2025, 4:07 PM 
table filled with natural numbers, we say it is a divisor table if:
-th row are exactly all the divisors of some natural number 
,
-th column are exactly all the divisors of some natural number 
,
for every 
.
is given. Determine the smallest natural number , divisible by , such that there exists an divisor table, or prove that such does not exist.by SunnyEvan, Apr 1, 2025, 9:54 AM 
, 
, 
be non-negative real numbers, no two of which are zero. Prove that :
by parmenides51, Mar 26, 2024, 3:48 PM 
squares with two game pieces. At the beginning, Alice’s piece is on the first square while Bob’s piece is on the last square. The figure shows the starting position for a strip of 
squares.
can Bob ensure a win no matter how Alice plays? can Alice ensure a win no matter how Bob plays?by pieater314159, Jun 19, 2019, 8:08 PM 
be a polynomial with integer coefficients such that 
, and let 
be an integer. Define 
and 
for all integers 
. Show that there are infinitely many positive integers such that 
.by danepale, Apr 25, 2016, 6:39 PM 
be an acute triangle with circumcenter 
. Points 
and 
are chosen on segments 
and 
such that 
. If 
is the midpoint of the arc 
and 
is the midpoint of the arc 
, prove that 
.The oldest, shortest words — "yes" and "no" — are those which require the most thought.
February 2021
March 2020
February 2018
January 2018
November 2017
September 2017
July 2017
June 2017
May 2017
April 2017
March 2017
February 2017
December 2016
April 2016
such that 
coprime, 
and 
.
April 2021