Glaisher's theorem is a result in number theory useful to the study of integer partitions. Proved in 1883 by James Whitbread Lee Glaisher, it states that the number of partitions of an integer into parts not divisible by some number d equals the number of partitions in which no part is repeated d or more times. The result generalizes an earlier 1748 finding of Leonhard Euler for the case where d equals 2, the statement that the number of partitions into distinct parts equals the number of partitions into odd parts. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/
Facts
StatementThe number of partitions of n into parts not divisible by d equals the number of partitions in which no part is repeated d or more times. 2 Classification
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Entity-backed identity for the statement-form enum value this theorem already carries, resolved to a mathematics concept by an explicit value-to-entity map (phase 3 bucket conversion, docs\design_entity_backed_browse_buckets_20260928.md). The statement-form fact itself stays on the theorem unchanged.
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Source Glaisher's theorem (Wikipedia)
Sources
1. Wikipedia: Glaisher's theorem
WikipediaLead section, statement-form referenceQuote, Lead section, statement-form reference
Proved in 1883 by James Whitbread Lee Glaisher, it states that the number of partitions of an integer n into parts not divisible by d is equal to the number of partitions in which no part is repeated d or more times.
2. Glaisher's theorem (Wikipedia)
Statement
is equal to the number of partitions in which no part is repeated d or more times
Introduction, first sentence
Proved in 1883 by James Whitbread Lee Glaisher
In Branch: Number Theory, Lead sentence
In number theory, Glaisher's theorem is an identity useful to the study of integer partitions.
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