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.
