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3
prime no. expression
prime no. expression
Source:
October 15, 2010
number theory unsolved
number theory
Problem Statement
Prove that a prime
p
p
p
is expressible in the form
x
2
+
3
y
2
;
x
,
y
∈
Z
x^2+3y^2;x,y\in Z
x
2
+
3
y
2
;
x
,
y
∈
Z
if and only if it is expressible in the form
m
2
+
m
n
+
n
2
;
m
,
n
∈
Z
m^2+mn+n^2;m,n \in Z
m
2
+
mn
+
n
2
;
m
,
n
∈
Z
.Can
p
p
p
be replaced by a natural number
n
n
n
?
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