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

DOI:
https://doi.org/10.1090/S0002-9939-09-09990-0

Published electronically:
June 25, 2009

MathSciNet review:
2529860

Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: For any integer , let denote the triangular number . In this paper we give a complete characterization of all the triples of positive integers for which the ternary sums 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:
https://doi.org/10.1090/S0002-9939-09-09990-0

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