mersenneforum.org Mersenne primes and irreducible polynomials
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 2013-10-29, 10:19 #1 Nick     Dec 2012 The Netherlands 5·353 Posts Mersenne primes and irreducible polynomials This was a recent homework question at Leiden University which may appeal to members of this forum: (a) Let p be a positive integer. Assume that $2^p-1$ is a prime number and that $X^p+X+1\in\mathbb{F}_2[X]$ is irreducible. Prove that $X^{2^p-1}+X+1\in\mathbb{F}_2[X]$ is irreducible. (b) Prove that the polynomial $X^{2^{2^{2^{2^2-1}-1}-1}-1}+X+1$ is irreducible over $\mathbb{F}_2$.

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