Glaisher's theorem
Encyclopedia
In number theory
, Glaisher's theorem is an identity useful to the study of integer partitions. It is named for James Whitbread Lee Glaisher
.
It states that the number of partitions of an integer
into parts not divisible by 
is equal to the number of partitions of the form
where
and
that is, partitions in which no part is repeated d or more times.
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
, Glaisher's theorem is an identity useful to the study of integer partitions. It is named for James Whitbread Lee Glaisher
James Whitbread Lee Glaisher
James Whitbread Lee Glaisher son of James Glaisher, the meteorologist, was a prolific English mathematician.He was educated at St Paul's School and Trinity College, Cambridge, where he was second wrangler in 1871...
.
It states that the number of partitions of an integer
into parts not divisible by is equal to the number of partitions of the formwhere
and
that is, partitions in which no part is repeated d or more times.