.
?
?
(i.e., the square on 
has 
,
,
to the centers of the opposite squares are concurrent.
be the solid square region with vertices at![\[
(0, 0), \left(\frac{1}{2}, \frac{1}{2}\right), (1, 0), \left(\frac{1}{2}, -\frac{1}{2}\right).
\]](http://latex.artofproblemsolving.com/a/9/8/a9898f9237f07eaef5d17a9ac689d80ca631863f.png)
consists of two copies of 
:
counterclockwise around the origin and scaled by a factor of 
,
.
below.
be the limiting region of the sequence 
.
for relatively prime positive integers 
and 
.
.
,
.
.
be prime numbers such that![\[
\frac{1}{pq}+\frac{1}{qr}+\frac{1}{pr}=\frac{1}{839}
\]](http://latex.artofproblemsolving.com/b/6/f/b6f882f3c93b0877419db625c2a427fc9561605b.png)
Hence find the numbers of ordered triples 
,
equal to 
,
equal to 
.
, where 
.
for all real numbers 
satisfying the equation 
is:
be positive integers such that
Find the maximum possible value of 
.
Y by cursed_tangent1434, NicoN9, EeEeRUT
I hope posting this in Site Support is fine? I'm not sure whether an HSO admin is doing this but-
The EGMO 2025 problem 1 and problem 2 were originally posted by me on the day of the contest and found deleted (not by me) yesterday. Someone else noticed this and posted the problems again, but these threads were deleted once more.
The EGMO 2025 problem 1 and problem 2 were originally posted by me on the day of the contest and found deleted (not by me) yesterday. Someone else noticed this and posted the problems again, but these threads were deleted once more.
