![\[ x + y^2 = p^m \]](http://latex.artofproblemsolving.com/e/c/f/ecf553036f22327dd457dc06611b6bc1b0ef072c.png)
![\[ x^2 + y = p^n \]](http://latex.artofproblemsolving.com/5/b/d/5bd672934a395aabd6865ca4b50d8da75c0fe07e.png)
For 
positive integers and 
being a prime.
and 
.
Equality holds when 
or 
,
,
and 
lie on a circle 
such that 
.
at 
and 
.
intersect again at 
.
.
Equality holds when 
Y by Adventure10
In 
, angle bisector 
is drawn. The tangent at 
to the circumcircle 
of the triangle 
intersects the side 
at the point 
. The line 
intersects at 
. Prove that the line 
passes through the midpoint of the segment 
.
, angle bisector 
is drawn. The tangent at 
to the circumcircle 
of the triangle 
intersects the side 
at the point 
. The line 
intersects at 
. Prove that the line 
passes through the midpoint of the segment 
.This post has been edited 2 times. Last edited by parmenides51, Jun 21, 2022, 2:28 AM
,
tangent line 
.
,
,
