Glaisher's theorem

In number theory, Glaisher's theorem is an identity 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 ${\displaystyle n}$ into parts not divisible by ${\displaystyle d}$ is equal to the number of partitions in which no part is repeated ${\displaystyle d}$ or more times. This generalizes a result established in 1748 by Leonhard Euler for the case ${\displaystyle d=2}$.