Wikipedia:Reference desk/Archives/Mathematics/2013 July 11

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July 11

Gödel's incompleteness theorems

What does the term "complete" mean in this context and how does it contrast with "consistent"? — Melab±1 ☎ 04:37, 11 July 2013 (UTC)

Consistent means that a contradiction can't be derived. Complete means that every statement that can be formed in the system can be proven to be either true or false. Bubba73 ^{You talkin' to me?} 04:45, 11 July 2013 (UTC)

See complete theory and consistency. Gandalf61 (talk) 12:15, 11 July 2013 (UTC)

Generalisations of Fermat's Last Theorem?

Are there any findings about when the sum of kth powers of three or more positive integers can equal to another positive integer's kth power?like that in this book

Do Fermat's Last Theorem also apply to complex numbers?--128.237.207.243 (talk) 21:29, 11 July 2013 (UTC)

Are you referring to complex numbers of the form Z², whose real and imaginary parts are both integers ? — 79.113.215.215 (talk) 23:11, 11 July 2013 (UTC)

Also known as Gaussian integers.--80.109.106.49 (talk) 23:12, 11 July 2013 (UTC)

Yes, it should be --128.237.137.221 (talk) 23:33, 11 July 2013 (UTC)

See

Euler's sum of powers conjecture#Generalizations

Beal's conjecture

Jacobi–Madden equation

Prouhet–Tarry–Escott problem

Taxicab number

and these relevant Google results for its extension to Gaussian integers

— 79.113.210.229 (talk) 01:37, 12 July 2013 (UTC)

Also Pythagorean quadruple. Duoduoduo (talk) 18:56, 14 July 2013 (UTC)