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

2 votes

How long does it take to compute a class number?

Index calculus works, and much faster (although it is randomized); search for "subexponential class group".
Edgardo's user avatar
  • 276
6 votes

The intersection of a circle and a rank 3 subgroup of the plane

Here's at least a method that probably solves the problem. I say "probably" because I'm not entirely confident in my treatment of degenerate cases. Anyway, the main idea is to try to construct a secon …
Edgardo's user avatar
  • 276