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.
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StatementIf 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 FormCharacterization Theorem 1 Skolem-Mahler-Lech Theorem
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Source Skolem-Mahler-Lech Theorem (Wikipedia)
Source Skolem-Mahler-Lech Theorem (Wikipedia)
Proved By
Source Skolem-Mahler-Lech Theorem (Wikipedia)
Source Skolem-Mahler-Lech Theorem (Wikipedia)
Sources
1. Skolem-Mahler-Lech Theorem (Wikipedia)
Wikimedia FoundationLead 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
View the Source Skolem-Mahler-Lech Theorem (Wikipedia)
Principal Result Of: Thoralf Skolem, Lead sentence of the article on the result
This result is named after Thoralf Skolem (who proved the theorem for sequences of rational numbers), Kurt Mahler (who proved it for sequences of algebraic numbers), and Christer Lech (who proved it for sequences with values in any field of characteristic zero.
Principal Result Of: Kurt Mahler, Lead sentence of the article on the result
This result is named after Thoralf Skolem (who proved the theorem for sequences of rational numbers), Kurt Mahler (who proved it for sequences of algebraic numbers), and Christer Lech (who proved it for sequences with values in any field of characteristic zero.
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