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By $MRDP$ resolution of Hilbert's tenth, we infer, counting number of solutions to Diophantine equations is undecidable. Is parity of number of solutions to Diophantine equations undecidable?

Hilbert 10th problem, while undecidable in general, remains open for 2-variable equations: we do not know if there is an algorithm that, for polynomial $P(x,y)$ with integer coefficients, decides ...

Suppose I have a real number $$ x=\sum_{i=1}^n a_i e^{\lambda_i} $$ where $a_i,\lambda_i$s are complex algebraic numbers. Is there an algorithm to determine whether it is greater than 0 or less than ...

(I asked this a little over 3 months ago on math.SE, and when I initially re-asked here, no one had responded there. $\:$ After I re-asked here, Eric Towers responded there, since I had forgotten to ...