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Euclidean, hyperbolic, discrete, convex, coarse geometry, metric spaces, comparisons in Riemannian geometry, symmetric spaces.

6 votes

Line-preserving bijection of ${\mathbb{R}}^n$ onto itself

Do you assume that $f$ is surjective? Else, $f(x,y)=(x^3+y,0)$ would send any line to the $x$-axis.
Lev Borisov's user avatar
  • 5,186
3 votes

Three questions concerning lattice points on sphere surfaces

It is not really my area, but the answer to part 2 is that you are looking for the smallest $N$ such that there are exactly $8n-4$ ways of writing it in the form $a^2+b^2$. If such $N$ is even but i …
Lev Borisov's user avatar
  • 5,186