A
P
k
{P_k}
-set of size n is a set
{
x
1
,
…
,
x
n
}
\{ {x_1}, \ldots ,{x_n}\}
of distinct positive integers such that
x
i
x
j
+
k
{x_i}{x_j} + k
is a perfect square, whenever
i
≠
j
i \ne j
; a
P
k
{P_k}
-set X can be extended if there exists
y
∉
X
y \notin X
such that
X
∪
{
y
}
X \cup \{ y\}
is still a
P
k
{P_k}
-set. The most famous result on
P
k
{P_k}
-sets is due to Baker and Davenport, who proved that the
P
1
{P_1}
-set 1, 3, 8, 120 cannot be extended. In this paper, we show, among other things, that if
k
≡
2
(
mod
4
)
k \equiv 2\;\pmod 4
, then there does not exist a
P
k
{P_k}
-set of size 4, and that the
P
−
1
{P_{ - 1}}
-set 1, 2, 5 cannot be extended.