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problem

Define a monic irreducible polynomial with integral coefficients to be a polynomial with leading coefficient 1 that cannot be factored, and the prime factorization of a polynomial with leading coefficient 1 as the factorization into monic irreducible polynomials. How many not necessarily distinct monic irreducible polynomials are there in the prime factorization of (x8+x4+1)(x8+x+1)\left(x^{8}+x^{4}+1\right)\left(x^{8}+x+1\right) (for instance, (x+1)2(x+1)^{2} has two prime factors)?
Plain-text mathematical notation (without MathML)
Define a monic irreducible polynomial with integral coefficients to be a polynomial with leading coefficient 1 that cannot be factored, and the prime factorization of a polynomial with leading coefficient 1 as the factorization into monic irreducible polynomials. How many not necessarily distinct monic irreducible polynomials are there in the prime factorization of (x⁸+x⁴+1)(x⁸+x+1) (for instance, (x+1)² has two prime factors)?
Original LaTeX notation
Define a monic irreducible polynomial with integral coefficients to be a polynomial with leading coefficient 1 that cannot be factored, and the prime factorization of a polynomial with leading coefficient 1 as the factorization into monic irreducible polynomials. How many not necessarily distinct monic irreducible polynomials are there in the prime factorization of $\left(x^{8}+x^{4}+1\right)\left(x^{8}+x+1\right)$ (for instance, $(x+1)^{2}$ has two prime factors)?

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Source and history

task_id
e859b559-c649-5e54-9955-c2b153a8267c
task_key
test--e859b559-c649-5e54-9955-c2b153a8267c
task_revision_id
1
config / split
/ test

Official source

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