![\[ x + y^2 = p^m \]](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, Mango247
Given a parallelogram 
. A certain circle passes through points 
and 
and intersects the segments 
and 
the second time in the points 
and 
, and the circumscribed circle of the triangle 
crosses the segment for the second time at the point 
. Prove that the segments 
and 
are equal.
. A certain circle passes through points 
and 
and intersects the segments 
and 
the second time in the points 
and 
, and the circumscribed circle of the triangle 
crosses the segment for the second time at the point 
. Prove that the segments 
and 
are equal.This post has been edited 1 time. Last edited by parmenides51, Sep 13, 2018, 7:36 PM
Reason: name typo
Reason: name typo
giving 
.
