[/quote]
,
be a triangle. Let 
be a circle passing through 
intersecting 
at 
and 
at 
.
be the intersection of 
and 
and 
be the intersections of 
and 
with the tangent to 
at 
.
be the second intersection of 
and 
and 
be a polynomial with integer coefficients such that 
,
be an integer. Define 
and 
for all integers 
.
such that 
.
such that 
coprime, 
and 
.
![\[
\text{Find all functions } f : \mathbb{R} \to \mathbb{R} \text{ such that:} \\
f(a^4 + a^2b^2 + b^4) = f\left((a^2 - f(ab) + b^2)(a^2 + f(ab) + b^2)\right)
\]](http://latex.artofproblemsolving.com/2/a/7/2a73a5e58eab4a994fbd83160fb79a0b00152951.png)
table filled with natural numbers, we say it is a divisor table if:
-
,
-
,
for every 
.
is given. Determine the smallest natural number 
.
and 
such that 
.
and 
,
.
,
,
be non-negative real numbers, no two of which are zero. Prove that :
is the cube of a positive integer. Find 
Y by Exponent11, Alex-131, Pengu14, squareman, Danielzh, NaturalSelection, EpicBird08, ESAOPS, Everestbaker, scannose, KenWuMath, DhruvJha, crazyeyemoody907
Hello to all creative problem solvers,
Do you want a life changing math experience?
Do you want to see me in real life?
Check out the
Rutgers Expo in Problem Solving (REPS) by OMMC!
OMMC is presenting to you its next major event: in-person this time! This spring, OMMC is hosting its THIRD IN-PERSON event, where we will be presenting various speakers of math, holding breakout sessions, games and friendly competitions, and providing a math hub for people all over to learn and enjoy. No math experience is needed, and elementary, middle and high schoolers can all register!
The Rutgers Expo in Problem Solving will take place on June 7th, 1 PM.
The venue is the Science Engineering Complex at Rutgers New-Brunswick. This is 96 Frelinghuysen Rd, Piscataway, NJ 08854.
Event includes:
This event is completely FREE to all students!
Fill out the registration form linked below to sign-up for this event and answer some important questions.
https://docs.google.com/forms/d/e/1FAIpQLSeAr2Nul9MBO_adVzHN9Rsrc8yQEjzxPXZHZ-LUFf-zWcwR7A/viewform?usp=preview
Students from anywhere can attend, as long as you can commute to the venue. Email us at ommcofficial@gmail.com for any questions or concerns.
We can’t wait to see you there!
- REPS Team
OMMC’S 2025 EVENTS ARE SPONSORED BY:
Do you want a life changing math experience?
Do you want to see me in real life?
Check out the
Rutgers Expo in Problem Solving (REPS) by OMMC!
OMMC is presenting to you its next major event: in-person this time! This spring, OMMC is hosting its THIRD IN-PERSON event, where we will be presenting various speakers of math, holding breakout sessions, games and friendly competitions, and providing a math hub for people all over to learn and enjoy. No math experience is needed, and elementary, middle and high schoolers can all register!
The Rutgers Expo in Problem Solving will take place on June 7th, 1 PM.
The venue is the Science Engineering Complex at Rutgers New-Brunswick. This is 96 Frelinghuysen Rd, Piscataway, NJ 08854.
Event includes:
- Math speakers, including Richard Rusczyk, Dr. Christian Yongwhan Lim, and Dr. Yang Liu.
- Activities including estimathon and mini math competition WITH PRIZES
- Itinerary coming soon!
This event is completely FREE to all students!
Fill out the registration form linked below to sign-up for this event and answer some important questions.
https://docs.google.com/forms/d/e/1FAIpQLSeAr2Nul9MBO_adVzHN9Rsrc8yQEjzxPXZHZ-LUFf-zWcwR7A/viewform?usp=preview
Students from anywhere can attend, as long as you can commute to the venue. Email us at ommcofficial@gmail.com for any questions or concerns.
We can’t wait to see you there!
- REPS Team
OMMC’S 2025 EVENTS ARE SPONSORED BY:
- Nontrivial Fellowship
- Citadel
- Jane Street
This post has been edited 3 times. Last edited by DottedCaculator, May 16, 2025, 2:43 AM
