Talk:Diophantine equation

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Needs references. Geometry guy 23:32, 16 June 2007 (UTC)

tell me in the way to figure out the problem on his tomb theat tells how old he was when he died... please tell me how to do that problem

See here: Diophantus Tombstone Problem

[edit] Fibonacci Sequence and its Second Degree Diophantine Equation

Forty years ago I discovered that the Fibonacci Sequence (1, 1, 2, 3, 5, 8, etc) can be generated from the second degree Diophantine equation

    5k^2 -/+ 4 = m^2    where the -,+ is taken alternately.

The equation is a variation on Pell's, in that

    x^2 - ny^2 = +/-  4   instead of 1.

Walter Abetz 13:32, 19 November 2006 (UTC)

[edit] Arithmetic Geometry

I'm personally not clear on the distinction between Arithmetic Geometry and Algebraic Geometry, except some vague awareness that the former usually deals with rational points on varieties and the latter with more general algebraic structure. So I can kind of see why 'Arithmetic geometry' redirects to this page, since finding rational points on varieties is roughly speaking the same problem as solving Diophantine equations. But it'd be nice if someone who knows something about the subject could insert a paragraph or two on this page about it, if not create an actual page for it. Chenxlee (talk) 17:55, 11 February 2008 (UTC)