For integers 
and nonzero 
,
a least absolute remainder of 
modulo 
is an integer 
for which
 |
for some integer 
,
with 
as small as possible. Equivalently, 
is an integer nearest to 
, so
 |
If 
is a half-integer, there are two least absolute remainders with opposite signs. For
example, 
, so 
is a least absolute remainder of 47 modulo 10, whereas the
ordinary nonnegative remainder is 7. Repeated least
absolute remainders give a variant of the Euclidean
algorithm.
