The Fresneda Quiroga Conjecture

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.

4 thoughts on “The Fresneda Quiroga Conjecture

  1. I was duly attracted to this post, but saw in horror how you have attributed a Math competition exercise to my misspelled last name(s) – look at the link!- as a conjecture. However, as I didn’t find flaws on your proof I have to congratulate you once again, hoping next time I visit you correct your ways 🙂

    1. Hi Roman, I based your names faithfully on what is on “linked in” though it does seem that I added a hyphen please send me the correction if more is needed.

      In the post I reference the fact that this will be somebody else’s theorem. However, the enjoyment for me of this maths problem came from it being a conjecture of yours thus for me it remains “the Fresneda Quiorga conjecture”. Would I have enjoyed it as much to work through someone else’s proof?

    1. Hi Roman, I appreciate that you got this puzzle from somewhere – but I got it from you so on my blog it has your name until someone else (the true originator, say) provides me it’s real name. Obviously if you had shown me the proof I probably wouldn’t have called it the Fresneda-Quiroga Theorem (as I have not renamed it the Robinson Theorem) as Theorem is a more illustrious title whereas I think its fair to throw conjecture around willy-nilly.

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