with circumcircle 
,
that is tangent to segment 
at 
.
-
of 
is tangent to 
at 
.
is the midpoint of the arc 
,
.
have the same radius, then tangents to 
intersect on 
.
such that 
is a perfect square for all integers 
and 
.
such that for all 
the following holds:![\[f(x)+f(y)=f(xy)+f(f(x)+f(y))\]](http://latex.artofproblemsolving.com/a/c/a/aca098172ea7ce5663e9dd0dd10c2f1495630230.png)
be a convex hexagon, such that the triangles 
are equilateral and the diagonals 
and 
are concurrent. Prove that 
or 
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I'm free for a short while, other articles (or actually, problem sets) may come soon. 
Here are 100 Functional Equations Problems, and I dedicate it to pco.
See the attachment.
Here are 100 Functional Equations Problems, and I dedicate it to pco.
See the attachment.
This post has been edited 1 time. Last edited by Amir Hossein, Nov 21, 2017, 9:38 AM
Reason: Added the TeX file.
Reason: Added the TeX file.
,
,
,
,
be set of all primes
,
from 
