[/quote]
,
satisfying
Prove
is a positive integer. Call all positive divisors of 
and 
beautiful divisors and difference of any 
that verify the following equation for all 
:
be a triangle with incenter 
and circumcircle 
.
passing through 
and 
passing through 
of 
,
of 
and 
.
and 
meet at 
.
be a point such that 
is tangent to 
is tangent to 
are collinear.
.
When does equality hold?
denote the set of all positive integers less than 
that are relatively prime to 
.
reducible over the rational numbers, given that it has integer coefficients?
blocks, each weighing at least 
.
with 
you can choose a subset of the blocks whose total weight is at least 
.
such that 
.
.
be a subset of 
.
.
Y by centslordm
Let 
be a circle with the center of 
and 
be a point in the plane. Each line that passes through 
and intersects the circle , determines a chord with the circle. Show that the centers of all these chords lie on one and the same circle.
be a circle with the center of 
and 
be a point in the plane. Each line that passes through 
and intersects the circle , determines a chord with the circle. Show that the centers of all these chords lie on one and the same circle.This post has been edited 3 times. Last edited by parmenides51, May 29, 2021, 9:16 PM
and radius 
;
,
.
.
