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16Z

16Z denotes the set of all integers that are multiples of 16. Equivalently, 16Z = {16k : k ∈ Z}. It is a subgroup of the additive group of integers and, in the ring Z, it is the principal ideal generated by 16.

Because every element of 16Z can be written as 16k, the subgroup is infinite cyclic and is

Its index in Z is 16, since the cosets modulo 16 are [0], [1], ..., [15], and Z/16Z

Elements of 16Z are exactly the integers divisible by 16, such as ..., -32, -16, 0, 16, 32,

Other perspectives: in arithmetic, 16Z is the kernel of the reduction homomorphism Z → Z/16Z and appears

isomorphic
to
Z
via
the
map
k
↦
16k.
It
is
generated
by
16
as
an
additive
group.
has
16
elements.
The
quotient
by
16Z
identifies
integers
by
their
remainder
modulo
16.
48,
...
in
problems
involving
divisibility
and
modular
congruences.
As
a
subset
of
R,
16Z
forms
a
lattice
with
spacing
16.