The Kloosterman sum
\[
∑
x
=
0
;
(
x
,
p
)
=
1
p
α
−
1
exp
(
2
π
i
n
(
x
+
x
¯
)
/
p
α
)
,
\sum \limits _{x = 0;(x,p) = 1}^{{p^\alpha } - 1} {\exp (2\pi in(x + \bar x)/{p^\alpha }),}
\]
where p is an odd prime,
α
≧
2
\alpha \geqq 2
and
(
n
,
p
)
=
1
(n,p) = 1
, is evaluated in a very short direct way.