Fermat polygonal number theorem is that every positive integer is a sum of <=n n-gonal numbers (n such numbers seems to not be always needed, e.g. only needed 4 for n=6, so what is the smallest m such that every positive integer is a sum of <=m n-gonal numbers? I only know that m<=n), but what about centered n-gonal numbers and generalized n-gonal numbers (e.g. OEIS: A001318 for n=5), what is smallest number m such that every positive integer is a sum of <=m such numbers? Also, what about n-dimensional simplex numbers and n-dimensional cross-polytope numbers (generalization of Pollock's conjectures to higher dimension)? (For n-dimensional hypercube, there is already Waring's problem) 220.132.216.52 (talk) 12:09, 28 January 2025 (UTC)[reply]