+676 Looks like all of the unanswered questions have all been answered... Well.. I might shove a question onto here because the to-do list seems empty...
$$X^2 = Y+a$$
$$Y^2 = Z+a$$
$$Z^2 = X+a$$
It was an old question I remember from Early High School. Lets see what you guys come up with.
+118609
Thanks for the question Takahiro 
I cheated (or used the resources available to me)
http://www.wolframalpha.com/input/?i=X%5E2%3DY%2Ba%2C+Y%5E2%3DZ%2Ba%2C+Z%5E2%3DX%2Ba
It seems that the only real solution is
$$X=Y=Z=-n\\
a=n^2+n\\
\mbox{Where } n\;\in R$$
+118609
Thanks for the question Takahiro
I cheated (or used the resources available to me)
http://www.wolframalpha.com/input/?i=X%5E2%3DY%2Ba%2C+Y%5E2%3DZ%2Ba%2C+Z%5E2%3DX%2Ba
It seems that the only real solution is
$$X=Y=Z=-n\\
a=n^2+n\\
\mbox{Where } n\;\in R$$
