How do you find integer solutions to x/(y + z) + y/(x + z) + z/(x + y) = 4?

Re:How do you find integer solutions to x/(y + z) + y/(x + z... by DonbunEf7 on Sunday August 06, 2017 @10:52PM (#14944972)

Can you find (possibly negative) integers x, y, and z, such that x ^ 3 + y ^ 3 + z ^ 3 == 33? If so, it's publication-worthy.

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Re:How do you find integer solutions to x/(y + z) + y/(x + z... by bmc7505 on Monday August 07, 2017 @02:09AM (#14945639)

Is the constant 33 important (ie. would it be any less significant if it were 42, or 74 instead) and if so, why?

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Re:How do you find integer solutions to x/(y + z) + y/(x + z... by lifthrasiir on Monday August 07, 2017 @02:27AM (#14945694)

I was replying that the constants in question include 33, 42 and 74... and realized that I'm late :-) In a more recent survey, though, it is now known that:

> 74 = −284650292555885^3 + 66229832190556^3 + 283450105697727^3 [1] [2].

[1] https://arxiv.org/pdf/1604.07746v1.pdf

[2] https://mathoverflow.net/a/223121

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Re:How do you find integer solutions to x/(y + z) + y/(x + z... by skypather on Sunday August 06, 2017 @11:50PM (#14945199)

what if I can prove there is no integer solution for it? Is it still publication-worthy?

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Re:How do you find integer solutions to x/(y + z) + y/(x + z... by chx on Monday August 07, 2017 @12:02AM (#14945232)

Even more so!

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