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Old 2013-10-29, 10:19   #1
Nick
 
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Dec 2012
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Default 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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