"Aldrich" <aldrich617@...> wrote:

> I don't see how

> it immediately follows from Hardy/Wright Theorem 257 that

> A = 5x^2 + 5xy + y^2 has as values ALL of the possible

> values of primes that are +/- 1 mod 10.

Let w = (1+sqrt(5))/2 be the fundamental unit.

HW prove that every prime p = +/-1 mod 10 is of the form

norm(a+b*w) = a^2 + a*b - b^2

for some integer pair [a,b].

Lemma: Every prime p = +/-1 mod 10 is of the form

norm(2*x+y+x*w) = 5*x^2 + 5*x*y + y^2

for some integer pair [x,y].

Proof: Set x = b, y = a-2*b.

David