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On Graham partitions twisted by the Legendre symbolopen access
- Authors
- Kim, Byungchan; Kim, Ji Young; Lee, Chong Gyu; Lee, Sang June; Park, Poo-Sung; Park, Yoon Kyung
- Issue Date
- Oct-2023
- Publisher
- DE GRUYTER POLAND SP Z O O
- Keywords
- Graham partition; sum of reciprocals; quadratic twist; Legendre symbol; polygonal number
- Citation
- OPEN MATHEMATICS, v.21, no.1
- Journal Title
- OPEN MATHEMATICS
- Volume
- 21
- Number
- 1
- ISSN
- 2391-5455
- Abstract
- We investigate when there is a partition of a positive integer n, n = f(lambda(1)) + f(lambda(2))+& ctdot;+f(lambda(& ell;)),satisfying that 1 = chi(p)(lambda(1))/lambda(1 )+ chi(p)(lambda(2))/lambda(2)+& ctdot; + chi(p)(lambda(& ell;))/lambda(& ell;,)where chi(p) is the Legendre symbol modulo prime p and f(k) = k or the k th m -gonal number with m = 3, 4, or 5.
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Related Researcher
- Lee, Chong Gyu
- College of Natural Sciences (Department of Mathematics)