Talk:Erdős–Straus conjecture

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[edit] Correctness of a related conjecture

I very much doubt the correctness of this section in Generalization: Hagedorn proved a related conjecture of R. H. Hardin and Neil Sloane that, for odd positive n, the equation 3/n = 1/x + 1/y + 1/z is always solvable with x, y, and z also odd and positive. A proof of this conjecture would be trivial: Let x = y = z be n. Ocolon 22:33, 29 January 2007 (UTC)

x, y, and z must not equal each other. I edited in a clarification. —David Eppstein 03:16, 30 January 2007 (UTC)

[edit] Link to Leibniz harmonic triangle

A link was added to the Leibniz harmonic triangle. I wonder if this is relevant to the topic. The Leibniz harmonic triangle might be used to find solutions for n = 4m but the case is rather simple anyway: Ocolon 08:28, 4 March 2007 (UTC)

You stopped with that one case, but it can also be used to get solutions with distinct denominators. And with a little creativity, it can also help when 4|n is false. Anton Mravcek 20:10, 4 March 2007 (UTC)

While this might be true, neither the description of the link nor the article about the Leibniz harmonic triangle says that it can be used to find solutions for natural numbers that are not divisible by 4 or that it provides distinct denominators. Besides, the Erdős–Straus conjecture does not require distinct denominators. Furthermore, I don't understand this article as collection of solutions for special cases of the Erdős–Straus conjecture. Shall we add links that solve it for all Mersenne primes, for all numbers that are divisible by 1234, for all square numbers…

I don't question that the Leibniz harmonic triangle may be used to compute some solutions. I question the relevance of that — and even if it was relevant — the helpfulness of the link as the Leibniz harmonic triangle article stops where I stopped: Naming that simple case. Ocolon 08:32, 5 March 2007 (UTC)

I was wondering the same thing. Also, are there published sources connecting the Leibniz triangle to the 4/n problem, or is it just someone's original research? —David Eppstein 18:28, 4 March 2007 (UTC)

There probably aren't any published sources making the connection. It's too simple. The first Google Scholar result uses a complicated bunch of equations to show why the triangle is symmetrical. Even so, I wouldn't be as dismissive as calling this "just someone's original research." It's probably been rediscovered several times by several different people. Anton Mravcek 20:10, 4 March 2007 (UTC)