Almost universal ternary sums of triangular numbers
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- by Wai Kiu Chan and Byeong-Kweon Oh
- Proc. Amer. Math. Soc. 137 (2009), 3553-3562
- DOI: https://doi.org/10.1090/S0002-9939-09-09990-0
- Published electronically: June 25, 2009
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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.References
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Bibliographic Information
- Wai Kiu Chan
- Affiliation: Department of Mathematics and Computer Science, Wesleyan University, Middletown, Connecticut 06459
- MR Author ID: 336822
- 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
- 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
- © Copyright 2009 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 137 (2009), 3553-3562
- MSC (2000): Primary 11E12, 11E20
- DOI: https://doi.org/10.1090/S0002-9939-09-09990-0
- MathSciNet review: 2529860