Dr. Sardonicus, Thanks for solving my math problems. Your posts are greatly appreciated around here.
If you know of a degree 6 polynomial which has factors 0 or 1 mod 7, please post examples here.
Meanwhile, a degree 4 polynomial
x^4+7x^3x^27x+1 with Discriminant D = 415125 = 3^4*5^3*41
is 0, 1 or 4 (mod 5) for any x value and appears to have similar properties to the cyclotomic polynomial other than factors congruent to 4 (mod 5) of x^4+2x^3+4x^2+8x+16, a generalization of x^4+x^3+x^2+x+1 of the form a^4+ab^3+a^2b^2+a^3b+b^4. Would there be an easy way to generate polynomials with number fields the same as the cyclotomic polynomial of degree 4 or more generally n1?
EDIT: For x = 32, 1276705 = 5*19*89*151
Last fiddled with by carpetpool on 20170216 at 03:52
