We employ moving frames along pairs of curves at constant separation to derive various conditions for a curve to belong to the surface of a circular cylinder.
We employ moving frames along pairs of curves at constant separation to derive various conditions for a curve to belong to the surface of a circular cylinder.
Let [Formula: see text] be the maximal order of a number field. Belcher showed in the 1970s that every algebraic integer in [Formula: see text] is the sum of pairwise distinct units, if the unit equation [Formula: see text] has a non-trivial solution [Formula: see text]. We generalize this result and give applications to signed double-base digit expansions.
In this note we prove that a Mal'cev algebra is 2-supernilpotent ([1, 1, 1] = 0) if and only if it is polynomially equivalent to a special expanded group. This generalizes Gumm's result that a Mal'cev algebra is abelian if and only if it is polynomially equivalent to a module over a ring.