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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

3 votes

How did Ramanujan discover this identity?

How Ramanujan found the identity is, of course, a mystery, but with the intelligent use of a computer algebra system, many such identities can be found. I wrote an article about this. Two of the simpl …
Marc Chamberland's user avatar
5 votes
2 answers
2k views

Rational solutions to x^3 + y^3 + z^3 - 3xyz = 1

I can show that there infinitely many solutions to this equation. Is it possible that the set of rational solutions is dense?
Marc Chamberland's user avatar