Axiomatic WikiWWikiDDefinitionsEuler's totient function
Definition·D118
The number of residue classes modulo n that are invertible, equivalently coprime to n.
In words
Euler's totient of n is the number of units modulo n: how many residue classes are invertible.
Never needed: F03 · F04 · F05 · F06 · F08 · F10 · F11 · F12 · F13 · A03 · A04 · A05 · A07 · A08 · A09 (computed from the citation graph, not asserted).
Remarks
Well defined because the units form a finite group, so the cardinality exists. By L78 and T60,
equally counts the residues
with
: the classic definition. Values:
,
,
, and
for a prime
(L80). Defining
as the order of the group of units is what makes Euler's theorem
an immediate consequence of L36.