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Polynomials over the Rational Field: Irreducible Polynomial: Prove that the polynomial 1 + x + x^2 +... + x^(p-1), where is a prime number, is irreducible over the field of rational numbers.

Modern Algebra
Ring Theory (XXXV)
Polynomials over the Rational Field
Euclidean Ring
Irreducible Polynomial

Prove that the polynomial 1 + x + x^2 +... + x^(p-1), where is a prime number, is irreducible over the field of rational numbers.
( Hint:- Consider the polynomial 1 + (x + 1) + (1 + x)^2 +... + (1 + x)^(p-1), and use the Einstein Criterion.)

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It is the explanation for the polynomial 1 + x + x^2 +... + x^(p-1), where is a prime number,to be irreducible over the field of rational numbers.
The solution is given in detail.

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