[/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 
?
dividing by x
.
be a cyclic quadrilateral with 
and let 
and 
be the feet of altitudes from 
to the lines 
and 
,
bisects 
.
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 
Y by
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Idk, is it a good goal, I usually pass within 10 problems sooo
