Glaisher's Theorem

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.