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Part of 2009 Miklós Schweitzer

Problems(1)

Irreducible polynomial over Q

Source: Schweitzer 2009

Prove that the polynomial f(x) \equal{} \frac {x^n \plus{} x^m \minus{} 2}{x^{\gcd(m,n)} \minus{} 1} is irreducible over

\mathbb{Q}

for all integers

n > m > 0

algebrapolynomialsuperior algebrasuperior algebra unsolved