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PEN P Problems
21
21
Part of
PEN P Problems
Problems
(1)
P 21
Source:
5/25/2007
Let
A
A
A
be the set of positive integers of the form
a
2
+
2
b
2
a^2 +2b^2
a
2
+
2
b
2
, where
a
a
a
and
b
b
b
are integers and
b
≠
0
b \neq 0
b
=
0
. Show that if
p
p
p
is a prime number and
p
2
∈
A
p^2 \in A
p
2
∈
A
, then
p
∈
A
p \in A
p
∈
A
.
floor function
function
pigeonhole principle
quadratics
modular arithmetic
algebra
domain