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Old 2017-02-16, 03:46   #6
carpetpool's Avatar
Nov 2016

52·13 Posts

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^3-x^2-7x+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 n-1?

EDIT: For x = 32, 1276705 = 5*19*89*151

Last fiddled with by carpetpool on 2017-02-16 at 03:52
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