24381Re: Impossible to Prove ??
- Aug 11, 2012"Aldrich" <aldrich617@...> wrote:
> I don't see howLet w = (1+sqrt(5))/2 be the fundamental unit.
> 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.
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.
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