Re: a*x^n+b*y^n puzzle
- Hi Mike,
What about :
--- In email@example.com, "mikeoakes2" <mikeoakes2@...> wrote:
> Here is a small puzzle:-
> Find fixed integers a, b, x, y such that the expression
> is prime for all n in the range 1 <= n <= n_max,
> where n_max is to be as large as possible.
> Hint: n_max=9 is certainly achievable.
> -Mike Oakes
- --- In firstname.lastname@example.org,
"Robdine" <robdine@...> wrote:
> any rational prime that can be represented by the sumThere is only rational prime of the form a^2 + b^2 that yields
> of 2 squares (a^2+b^2) will define 4 gaussian primes
precisely 4 distinct Gaussian primes, namely 2 = 1^2 + 1^2.
If a^2 + b^2 is an odd rational prime, we have
8 [sic] asociates of the Gaussian prime z = a + I*b,
since we may mulitply it and its conjugate z = a - I*b
by the 4 units I, -I, -1, 1, obtaining 8 distinct
Gaussian integers that are prime.