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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 $p = 3$ .

A remark on B₂-sequences in GF[p,x]

John R. Burke (1995)

Acta Arithmetica

A remark on primitive roots and ramitfication

victor S. Albis González (1973)

Revista colombiana de matematicas

A stationary phase formula for exponential sums over $ℤ / p^{m} ℤ$ and applications to GL(3)-Kloosterman sums

Romuald Dąbrowski, Benji Fisher (1997)

Acta Arithmetica

A Stickelberger theorem for p-adic Gauss sums

Régis Blache (2005)

Acta Arithmetica

Abriß einer arithmetischen Theorie der Galoisschen Körper. (Zweite Mitteilung)

Ö. Ore (1930)

Mathematische Annalen

Abriß einer arithmetischen Theorie der Galoisschen Körper. (Erste Mitteilung)

Ö. Ore (1928)

Mathematische Annalen

Addendum to: v-adic Zeta Functions, L-series and Measures for Function Fields.

David Goss (1979)

Inventiones mathematicae

Addition theorems in F q [x].

Jörgen CHERLY (1975/1976)

Seminaire de Théorie des Nombres de Bordeaux

Addition theorems in Fq [x].

Jorgen Cherly (1977)

Journal für die reine und angewandte Mathematik

Algebraic continued fractions in $_{q} ((T^{- 1}))$ and recurrent sequences in $_{q}$

Alain Lasjaunias (2008)

Acta Arithmetica

Almost primality of group orders of elliptic curves defined over small finite fields.

Koblitz, Neal (2001)

Experimental Mathematics

An Addition Theorem for the Elementary Abelian Group of Type (p, p).

Henry B. Mann, Ying Fou Wou (1986)

Monatshefte für Mathematik

An analogue of the Erdős-Ginzburg-Ziv theorem for quadratic symmetric polynomials.

Bialostocki, Arie, Tran Dinh Luong (2009)

Integers

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