What to do with a new mathematics conjecture? I have been working on a problem (not in mathematics) for a while and at the core there is a simply stated mathematical problem which I really cannot solve.  I have tried asking colleagues but they can't either. As far as I can tell it is not equivalent to some known problem either.  

I am not myself a professional mathematician so I see no prospect of my being able to solve it.  However I would love to know if it is true or not. Is there some forum to place non-trivial simply stated mathematical conjectures?  Or should I just put the whole paper on the arXiv and forget it?
"Is there some forum to place non-trivial simply stated mathematical conjectures?"  As far as I know , http://math.stackexchange.com can be a good place where to start.

If the methods required turn out to be more sophisticated, you can try asking on http://mathoverflow.net .

I am almost sure that on these sites you'll receive the right advices for your mathematical question