Theorem

Skolem-Mahler-Lech Theorem

Number Theory

For a linear recurrence sequence, the set of indices at which the sequence takes the value zero is, apart from finitely many exceptions, a union of full arithmetic progressions. Named for Thoralf Skolem, Kurt Mahler and Christer Lech, who each proved successive refinements.

Facts

Statement

If a sequence of numbers satisfies a linear recurrence with constant coefficients, then, with finitely many exceptions, the positions at which the sequence is zero form a finite union of arithmetic progressions. 1

Classification

Statement Form

Characterization Theorem 1

Connections

Source Skolem-Mahler-Lech Theorem (Wikipedia)

Thoralf Skolem

Source Skolem-Mahler-Lech Theorem (Wikipedia)

Sources

1. Skolem-Mahler-Lech Theorem (Wikipedia)

Wikimedia Foundation

Lead section
if a sequence of numbers satisfies a linear recurrence with constant coefficients, then with finitely many exceptions the positions at which the sequence is zero form a regularly repeating pattern.
Proved By: Thoralf Skolem, Lead paragraph
In algebraic number theory, the Skolem-Mahler-Lech theorem states that if a sequence of numbers satisfies a linear recurrence with constant coefficients, then
Proved By: Kurt Mahler, Lead paragraph
In algebraic number theory, the Skolem-Mahler-Lech theorem states that if a sequence of numbers satisfies a linear recurrence with constant coefficients, then with finitely

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Skolem-Mahler-Lech Theorem

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