On Universal Sums of Polygonal Numbers

@inproceedings{Sun2009OnUS,
  title={On Universal Sums of Polygonal Numbers},
  author={Zhi-Wei Sun},
  year={2009}
}
For m = 3, 4, . . . , the polygonal numbers of order m are given by pm(n) = (m−2) ( n 2 ) +n (n = 0, 1, 2, . . . ). For positive integers a, b, c and i, j, k > 3 with max{i, j, k} > 5, we call the triple (api, bpj , cpk) universal if for any n = 0, 1, 2, . . . there are nonnegative integers x, y, z such that n = api(x)+bpj(y)+cpk(z). We show that there are… CONTINUE READING