--- In

primenumbers@yahoogroups.com, "djbroadhurst" <d.broadhurst@...> wrote:

>

> Complex a*x^n+b*y^n puzzle: Find 4 Gaussian integers a,b,x,y

> such that x and y are not units and a*x^n+b*y^n is a Gaussian

> prime, for 1 <= n <= n_max, with n_max as large as possible.

Here is the output from complexification of yesterday's simple-minded pari-gp script, for n_max=9:-

a=3 + 3*I, b=2 + 3*I, x=2, y=1 - 2*I

n=1 u=14 + 5*I uu=221

n=2 u=18 - 5*I uu=349

n=3 u=-4 - 5*I uu=41

n=4 u=-38 + 75*I uu=7069

n=5 u=64 + 295*I uu=91121

n=6 u=558 + 455*I uu=518389

n=7 u=1276 - 85*I uu=1635401

n=8 u=722 - 1485*I uu=2726509

n=9 u=-3016 - 625*I uu=9486881

(u is your expression a*x^n+b*y^n, uu is its norm.)

Mike