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...
متن کامل5 M ay 2 00 9 Preprint , arXiv : 0905 . 0635 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 tr...
متن کاملA ug 2 00 9 Preprint , arXiv : 0905 . 0635 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...
متن کاملarXiv : 0906 . 2450 ON SOME UNIVERSAL SUMS OF GENERALIZED POLYGONAL NUMBERS
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 +...
متن کاملOn Almost Universal Mixed Sums of Squares and Triangular Numbers
In 1997 K. Ono and K. Soundararajan [Invent. Math. 130(1997)] proved that under the generalized Riemann hypothesis any positive odd integer greater than 2719 can be represented by the famous Ramanujan form x2 + y2+10z2; equivalently the form 2x+5y+4Tz represents all integers greater than 1359, where Tz denotes the triangular number z(z+1)/2. Given positive integers a, b, c we employ modular for...
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ژورنال
عنوان ژورنال: Science China Mathematics
سال: 2015
ISSN: 1674-7283,1869-1862
DOI: 10.1007/s11425-015-4994-4