Universal sums of generalized octagonal numbers
نویسندگان
چکیده
منابع مشابه
On Universal Sums of Polygonal Numbers
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 only 95 candidates for universal triple...
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For m = 3, 4, . . . those pm(x) = (m − 2)x(x − 1)/2 + x with x ∈ Z are called generalized m-gonal numbers. Recently the second author studied for what values of positive integers a, b, c the sum ap5 + bp5 + cp5 is universal over Z (i.e., any n ∈ N = {0, 1, 2, . . . } has the form ap5(x) + bp5(y) + cp5(z) with x, y, z ∈ Z). In this paper we proved that p5 + bp5 + 3p5 (b = 1, 2, 3, 4, 9) and p5 +...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2018
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2017.12.014