and
.
By using of trigonometric formulasSolution :
Put
and
.
By using of trigonometric formulas
and taking into account that
and
,
we have 
and
.
Therefore,
is
integer. If we define 
(mod
5) and 
(mod
5), then we have 
and
modulo
5. Obviously, 
is
uniquely determined by initial values
and
and
is a periodic sequence.
If
then
,
,
,
,
If
then
,
,
,
,
(Both sequences have a period 4). Finally, a = 1 or 4.