MathDB
Problems
Contests
National and Regional Contests
PEN Problems
PEN A Problems
38
38
Part of
PEN A Problems
Problems
(1)
A 38
Source:
5/25/2007
Let
p
p
p
be a prime with
p
>
5
p>5
p
>
5
, and let
S
=
{
p
−
n
2
∣
n
∈
N
,
n
2
<
p
}
S=\{p-n^2 \vert n \in \mathbb{N}, {n}^{2}<p \}
S
=
{
p
−
n
2
∣
n
∈
N
,
n
2
<
p
}
. Prove that
S
S
S
contains two elements
a
a
a
and
b
b
b
such that
a
∣
b
a \vert b
a
∣
b
and
1
<
a
<
b
1<a<b
1
<
a
<
b
.
floor function
Divisibility Theory