prove. Prove that the polynomial 1+x+x^ 2 +...+x^p-1 . where p is a prime number, is irreducible over the field of rational numbers.
prove. Prove that the polynomial 1+x+x^ 2 +...+x^p-1 . where p is a prime number, is irreducible over the field of rational numbers.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter8: Polynomials
Section8.4: Zeros Of A Polynomial
Problem 17E
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Note that we cannot directly apply Eisenstein criterion to prove.
Prove that the polynomial 1+x+x^ 2 +...+x^p-1 . where p is a prime number, is irreducible over the field of rational numbers.
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