be a cyclic quadrilateral with circumcentre 
.
and 
meet at point 
.
lie on a circle with centre 
.
are collinear.
such that, for all positive integers 
and 
,
be a positive integer. We say that 
such that:
for which![\[
a \mid s^b - l.
\]](http://latex.artofproblemsolving.com/5/d/9/5d9db7678c54d1c6a909b4aca39a329cadd71e2c.png)
2. For every proper divisor 
of 
and 
)![\[
a' \mid s^b - l.
\]](http://latex.artofproblemsolving.com/4/b/2/4b26b9bd3da8958287703c3f575bf5d5da7fd477.png)
Determine all bao-good positive integers 
such that![\[(a^2 + b^2 + c^2)^2 = 3(a^3b + b^3c + c^3a) + 1. \]](http://latex.artofproblemsolving.com/9/e/4/9e400fd807a9535ede983b75dcc307d8b75a35b6.png)
Y by Adventure10, Mango247
Let 
be some points which belong to the same circle. Prove that the following relations are equivalently;
![\[ WRONG \]](//latex.artofproblemsolving.com/b/1/8/b1889b5bb0bb8e2d3499a99c4c7f6c8247432768.png)
Remark: In the other message I will give the correct enunciation !
be some points which belong to the same circle. Prove that the following relations are equivalently;
![\[ WRONG \]](http://latex.artofproblemsolving.com/b/1/8/b1889b5bb0bb8e2d3499a99c4c7f6c8247432768.png)
Remark: In the other message I will give the correct enunciation !This post has been edited 5 times. Last edited by Virgil Nicula, Nov 13, 2005, 6:20 PM
be a convex cyclic hexagon. Prove that:
.
are similar, then
.
and
.
,
