is an acute angle triangle such that 
and 
.
the center of the circumscribed circle of the triangle and 
the intersection of altitudes of this triangle. Line 
intersects 
in point 
and 
in point 
.
.
.
be a point on side 
,
be a point on the extension of 
such that 
.
,
satisfying 
.
of positive integers with 
prime and ![\[ a^p=b!+p. \]](http://latex.artofproblemsolving.com/9/f/6/9f674dabcb364872cef4153198e2e362ae40a2fd.png)
Y by
The pyramid 
has base the rectangle ABCD, and the side edges are congruent. Prove that the plane 
forms congruent angles with the planes 
and 
if and only if 
.
has base the rectangle ABCD, and the side edges are congruent. Prove that the plane 
forms congruent angles with the planes 
and 
if and only if 
.This post has been edited 2 times. Last edited by parmenides51, May 19, 2020, 7:32 AM
