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such that there exists a unique integer 
such that 
with the following property:![\[ n!\mid a^n + 1
\]](http://latex.artofproblemsolving.com/e/2/3/e23d39aab685888993d355d8c93d4e6475f53487.png)
(use in a problem for junior) to practice. Can anyone share to me?
+1 w
be a square with 
side length and with center 
. A rhombus 
is drawn where point 
lies on line 
. What is the area of ?
be the incenter of a scalene triangle 
. In other words, 
are distinct. Prove that if 
are two points on rays 
, satisfying 
then line 
pass through the orthocenter of 
.
be the incenter of a scalene triangle . In other words, are distinct. Prove that if are two points on rays , satisfying then line pass through the orthocenter of .
be the midpoint of 
, and 
be the symmetrical point of 
against .
, 
is on one line.
line 
(angle bisector of 
) 
(angle bisector of 
).
, orthocenter of 
, is on the angle bisector of .
as 
is the excenter of , and we are done.
