MathOverflow

19 squared = 17 squared + 11 squared - 7 squared31 squared = 29 squared + 17 squared - 13 squared41 squared = 37 squared = 29 squared - 23 squared
in the same way
187631 squared = 187597 squared + 177209 squared - 177173 squared

In $\mathrm{Cl}(p,q,r)$ (geometric-algebra grading; $r$ = degeneratedirections, $e_0^2=0$) two infinitesimal structures seem to sit side by side intwo different parts of the same algebra.
Rotational symmetry. On the nondegenerate part, the grade-2 elements closeunder the commutator into a Lie algebra $\cong \mathfrak{so}(p,q)$, the Liealgebra of $\mathrm{Spin}$. This genuinely uses the Clifford product(contractions), not just the wedge...

We propose a tamer variant of the $3n + 1$ problem.
For simpler notation we write odd ($m$) for the resulting
odd number when dividing $m$ by $2$ as often as possible.

I have a proof in mathematical physics for a result that is widely used in the literature for the general $N$-layer case. However, the existing literature only provides a rigorous proof for the $N=2$ case, with the authors simply stating that the generalization...