The only nonassociative division algebra with real scalars. There is an 8-square identity corresponding to this algebra.
The elements of a Cayley algebra are called Cayley numbers or octonions, and the multiplication
table for any Cayley algebra over a field 
with field characteristic 
may be taken as shown in the following
table, where 
,
, ..., 
are a bases over 
and 
, 
, and 
are nonzero elements of 
(Schafer 1996, pp. 5-6).
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