[/quote]
,
satisfies the equation
,![\[
\frac{a}{b} + \frac{b}{c} + \frac{c}{a}.
\]](http://latex.artofproblemsolving.com/3/2/b/32b41635c159921e11245369e66185ec69b0d785.png)
with the following property: the sum of the elements of any finite subset of 
be the n-th prime number in increasing order for 
.
satisfying 
for all 
:
be real numbers that satisfy the condition:![\[
a_i \cdot a_j \geq i^2 - j^2 \quad \text{for all} \quad 1 \leq i \leq j \leq 2024.
\]](http://latex.artofproblemsolving.com/4/3/9/43970110f50d6fad23211b1ac099c128dca41636.png)
What is the minimum value of 
?
be a cyclic quadrilateral with 
and let 
and 
be the feet of altitudes from 
to the lines 
and 
,
bisects 
.
such that 
is an integer for every positive integer 
be an acute triangle. Points 
,
lie on a line in this order and satisfy 
.
and 
be the midpoints of 
and 
,
is acute, and let 
and 
and 
,
and 
and 
and 
for Girls, PRISMS Online Math Meet for Girls, is happening this spring! 
Y by forthegreatergood, ABCDE, minimario, ahaanomegas, Tan, Quadratic64, yugrey, pinetree1, blep, GeneralCobra19, Adventure10, sbicecream, parmenides51, Mango247, and 4 other users
We are pleased to announce that Kelvin the Frog has graciously signed a lucrative contract, finally allowing us to produce our mock AIME. Among other duties (such as taking a vacation from his Cartesian plane), Kelvin the Frog will be building various residences, constructing several infinite series, and playing with his friends Alex the Kat, Steven the Alpaca, AJ the Dennis the Menace, the Great Sabeenee, and the entire cast of unforgettable AAST characters.
As is typical for mock AIMEs, we follow the format of the actual AIME. There are 15 problems, roughly ordered by difficulty, to be solved over a continuous period of 3 hours. Obviously, this is run on the honor system. All answers are nonnegative integers ranging from 000 to 999, but due to computers deleting leading zeros anyway, they are not necessary to include (so 7, 07, and 007 are all acceptable answers).
This test will be released this weekend, on either late-ish Saturday or early-ish Sunday. This is because the test will (hopefully) be physically administered to the BCA math team this Saturday, so releasing it beforehand kind of defeats the purpose. Because this weekend is the last one before the actual AIME, submissions will stay open at least through (shortly before) the AIME II. You will, however, receive your score shortly after submission, and you are welcome to request solutions to specific problems. Obviously, you should not discuss the problems among people you cannot verify already submitted until otherwise announced.
As usual, there is a very distinct possibility that questions will be ambiguous, poorly worded, or just plain wrong. If you are certain that a problem does not have a valid answer (e.g. asks for
in the form 
, leads to a negative or 4-digit answer, asks for 
where 
is not squarefree, etc.), you should submit "1000" and an explanatory note. All answers that are not nonnegative integers with at most 3 digits besides 1000 will be immediately discarded, including submissions such as "seven" or "7\". Your answers are scored by program, so it is very important that you submit the ones you intend to. In the case of an ambiguity, pick any interpretation that leads to a valid answer, and submit that answer with an explanatory note.
After official answers/solutions and scores are released (which will be slightly after the AIME II) you will have an opportunity to protest. An acceptable protest must prove that your answer is undeniably correct (e.g. the burden of proof falls upon you), or that there is an alternate interpretation of the question leading to your answer. If your protest is accepted and you submitted the answer in the protest, your score (along with anyone who submitted that answer) will be incremented. You cannot, however, lose points for someone else successfully protesting a question (e.g. our answers will always be given credit).
There will be a google submission form available to submit your answers. We prefer that you use this form because it will contain some brief survey questions (e.g. "which problem did you find most difficult" and whatnot), but it is not required. You can also simply PM me your answers. Again, you will receive your score as soon as you are graded, and you can ask for specific solutions (the earlier you do this, the more likely you are to receive outlines rather than rigorous solutions however).
You do not have to sign up to take this, nor do you have to take it if you sign up. However, if you believe that you will take the test under contest conditions, signing up would be nice so we have a general idea of the number of participants.
On a completely unrelated note, I saved my 7000th post for this so you should all take it
As is typical for mock AIMEs, we follow the format of the actual AIME. There are 15 problems, roughly ordered by difficulty, to be solved over a continuous period of 3 hours. Obviously, this is run on the honor system. All answers are nonnegative integers ranging from 000 to 999, but due to computers deleting leading zeros anyway, they are not necessary to include (so 7, 07, and 007 are all acceptable answers).
This test will be released this weekend, on either late-ish Saturday or early-ish Sunday. This is because the test will (hopefully) be physically administered to the BCA math team this Saturday, so releasing it beforehand kind of defeats the purpose. Because this weekend is the last one before the actual AIME, submissions will stay open at least through (shortly before) the AIME II. You will, however, receive your score shortly after submission, and you are welcome to request solutions to specific problems. Obviously, you should not discuss the problems among people you cannot verify already submitted until otherwise announced.
As usual, there is a very distinct possibility that questions will be ambiguous, poorly worded, or just plain wrong. If you are certain that a problem does not have a valid answer (e.g. asks for
in the form 
, leads to a negative or 4-digit answer, asks for 
where 
is not squarefree, etc.), you should submit "1000" and an explanatory note. All answers that are not nonnegative integers with at most 3 digits besides 1000 will be immediately discarded, including submissions such as "seven" or "7\". Your answers are scored by program, so it is very important that you submit the ones you intend to. In the case of an ambiguity, pick any interpretation that leads to a valid answer, and submit that answer with an explanatory note.After official answers/solutions and scores are released (which will be slightly after the AIME II) you will have an opportunity to protest. An acceptable protest must prove that your answer is undeniably correct (e.g. the burden of proof falls upon you), or that there is an alternate interpretation of the question leading to your answer. If your protest is accepted and you submitted the answer in the protest, your score (along with anyone who submitted that answer) will be incremented. You cannot, however, lose points for someone else successfully protesting a question (e.g. our answers will always be given credit).
There will be a google submission form available to submit your answers. We prefer that you use this form because it will contain some brief survey questions (e.g. "which problem did you find most difficult" and whatnot), but it is not required. You can also simply PM me your answers. Again, you will receive your score as soon as you are graded, and you can ask for specific solutions (the earlier you do this, the more likely you are to receive outlines rather than rigorous solutions however).
You do not have to sign up to take this, nor do you have to take it if you sign up. However, if you believe that you will take the test under contest conditions, signing up would be nice so we have a general idea of the number of participants.
On a completely unrelated note, I saved my 7000th post for this so you should all take it
