A work colleague posed a puzzle a few months ago which was to prove that every positive integer can be expressed by a function of a and b with b plus the square of a divided by a plus the square of b. It has taken some time but following my recent change of sleep pattern I finished the proof earlier today. As is so often the case with these maths problems once one has found the solution it is so hard to understand why it was not obvious at the beginning. If anyone finds a mistake in the logic I would be keen to hear it. The Fresneda Quironga Conjecture (or at least my proof of what is likely someone else’s theorem) can be found by clicking the link.