A recursive definition of \(p\)-ary addition without carry (Q1975044)

Let \(p\) be a prime number. The \(p\)-ary addition without carry takes place in the theory of some generalized Nim-games, in the theory of some greedy codes, as well as in the determination of the least possible size of the sumset of two subsets of \((\mathbb Z/p\mathbb Z)^n\) with given cardinality. The author proves that for any \(p,\) there exists a recursive definition for this operation, as it was already known for \( p=2\) and \( p=3\) (for \(p=2, a+b= \min\{N \subset \{a'+b,a+b'; a'<a, b'<b\}\}).\) This provides a definition ``à la Conway'' of prime numbers.