Abstract
Let
Q
(
x
)
=
Q
(
x
1
,
x
2
,
…
,
x
n
)
be a nonsingular quadratic form with integer coefficients,
n
be even and
p
be an odd prime. In Hakami (J. Inequal. Appl. 2014:290, 2014, doi:
10.1186/1029-242X-2014-290
) we obtained an upper bound on the number of integer solutions of the congruence
Q
(
x
)
≡
0
(
mod
p
2
)
in small boxes of the type
{
x
∈
Z
p
2
n
|
a
i
⩽
x
i
<
a
i
+
m
i
,
1
⩽
i
⩽
n
}
, centered about the origin, where
a
i
,
m
i
∈
Z
,
0
<
m
i
≤
p
2
,
1
⩽
i
⩽
n
. In this paper, we shall drop the hypothesis of ‘centered about the origin’ and generalize the result of paper Hakami (J. Inequal. Appl. 2014:290, 2014, doi:
10.1186/1029-242X-2014-290
) to boxes of arbitrary size and position.