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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Almost universal ternary sums of triangular numbers


Authors: Wai Kiu Chan and Byeong-Kweon Oh
Journal: Proc. Amer. Math. Soc. 137 (2009), 3553-3562
MSC (2000): Primary 11E12, 11E20
Published electronically: June 25, 2009
MathSciNet review: 2529860
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Abstract: For any integer $ x$, let $ T_x$ denote the triangular number $ \frac{x(x+1)}{2}$. In this paper we give a complete characterization of all the triples of positive integers $ (\alpha, \beta, \gamma)$ for which the ternary sums $ \alpha T_x + \beta T_y + \gamma T_z$ represent all but finitely many positive integers, which resolves a conjecture of Kane and Sun.


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Additional Information

Wai Kiu Chan
Affiliation: Department of Mathematics and Computer Science, Wesleyan University, Middletown, Connecticut 06459
Email: wkchan@wesleyan.edu

Byeong-Kweon Oh
Affiliation: Department of Mathematical Sciences, Seoul National University, Seoul 151-747, Korea
Email: bkoh@math.snu.ac.kr

DOI: http://dx.doi.org/10.1090/S0002-9939-09-09990-0
PII: S 0002-9939(09)09990-0
Received by editor(s): August 28, 2008
Published electronically: June 25, 2009
Additional Notes: The work of the second author was supported by the Korea Research Foundation Grant (KRF-2008-314-C00004) funded by the Korean Government.
Communicated by: Wen-Ching Winnie Li
Article copyright: © Copyright 2009 American Mathematical Society