# A recursive definition of $p$-ary addition without carry

Journal de théorie des nombres de Bordeaux (1999)

- Volume: 11, Issue: 2, page 307-315
- ISSN: 1246-7405

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topLaubie, François. "A recursive definition of $p$-ary addition without carry." Journal de théorie des nombres de Bordeaux 11.2 (1999): 307-315. <http://eudml.org/doc/248328>.

@article{Laubie1999,

abstract = {Let $p$ be a prime number. In this paper we prove that the addition in $p$-ary without carry admits a recursive definition like in the already known cases $p = 2$ and $p = 3$.},

author = {Laubie, François},

journal = {Journal de théorie des nombres de Bordeaux},

keywords = {-ary representations of integers},

language = {eng},

number = {2},

pages = {307-315},

publisher = {Université Bordeaux I},

title = {A recursive definition of $p$-ary addition without carry},

url = {http://eudml.org/doc/248328},

volume = {11},

year = {1999},

}

TY - JOUR

AU - Laubie, François

TI - A recursive definition of $p$-ary addition without carry

JO - Journal de théorie des nombres de Bordeaux

PY - 1999

PB - Université Bordeaux I

VL - 11

IS - 2

SP - 307

EP - 315

AB - Let $p$ be a prime number. In this paper we prove that the addition in $p$-ary without carry admits a recursive definition like in the already known cases $p = 2$ and $p = 3$.

LA - eng

KW - -ary representations of integers

UR - http://eudml.org/doc/248328

ER -

## References

top- [1] C.L. Bouton, Nim, a game with a complete mathematical theory. Ann. Math. Princeton3 (1902), 35-39. Zbl32.0225.02MR1502275JFM32.0225.02
- [2] J.H. Conway, N.J.A. Sloane, Lexicographic Codes, Error Corrrecting Codes from Game Theory. IEEE Trans. Inform. Theory32 (1986), 337-348. Zbl0594.94023MR838197
- [3] S. Eliahou, M. Kervaire, Sumsets in vector spaces over finite fields. J. Number Theory71 (1998), 12-39. Zbl0935.11003MR1631038
- [4] F. Laubie, On linear greedy codes. to appear.
- [5] H.W. Lenstra, Nim Multiplication. Séminaire de Théorie des Nombres de Bordeaux 1977-78, exposé 11, (1978). Zbl0395.90119MR550271
- [6] V. Levenstein, A class of Systematic Codes. Soviet Math Dokl.1 (1960), 368-371. Zbl0095.11503MR122629
- [7] S.Y.R. Li, N-person Nim and N-person Moore's Games. Int. J. Game Theory7 (1978), 31-36. Zbl0382.90101MR484458
- [8] E.H. Moore, A generalization of the Game called Nim. Ann. Math. Princeton11 (1910), 93-94. Zbl41.0263.02MR1502397JFM41.0263.02

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