Skolem–Mahler–Lech theorem
Encyclopedia
In additive number theory
, the Skolem–Mahler–Lech theorem, named after Thoralf Skolem
, Kurt Mahler
, and Christer Lech, states that the indices of the null elements of a linear recurrence sequence
are the union of a finite set and finitely many arithmetic progression
s. The proofs of this result use p-adic analysis
.
Additive number theory
In number theory, the specialty additive number theory studies subsets of integers and their behavior under addition. More abstractly, the field of "additive number theory" includes the study of Abelian groups and commutative semigroups with an operation of addition. Additive number theory has...
, the Skolem–Mahler–Lech theorem, named after Thoralf Skolem
Thoralf Skolem
Thoralf Albert Skolem was a Norwegian mathematician known mainly for his work on mathematical logic and set theory.-Life:...
, Kurt Mahler
Kurt Mahler
Kurt Mahler was a mathematician and Fellow of the Royal Society.He was a student at the universities in Frankfurt and Göttingen, graduating with a Ph.D...
, and Christer Lech, states that the indices of the null elements of a linear recurrence sequence
Recurrence relation
In mathematics, a recurrence relation is an equation that recursively defines a sequence, once one or more initial terms are given: each further term of the sequence is defined as a function of the preceding terms....
are the union of a finite set and finitely many arithmetic progression
Arithmetic progression
In mathematics, an arithmetic progression or arithmetic sequence is a sequence of numbers such that the difference between the consecutive terms is constant...
s. The proofs of this result use p-adic analysis
P-adic analysis
In mathematics, p-adic analysis is a branch of number theory that deals with the mathematical analysis of functions of p-adic numbers....
.