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9 votes
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Semi-primes represented by quadratic polynomials

According to Lemke-Oliver, irreducible quadratic polynomials $G$ with positive leading coefficient and $\rho(2)<2$, (where $\rho(m)$ denotes the number of incongruent solutions to the congruence $G(...
Delmastro's user avatar
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5 votes
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Is there a polynomial version of Wilson's theorem which can avoid Cramer flavored conjectures?

Wilson's theorem states that a natural number $n > 1$ is a prime number if and only if the product of all the positive integers less than $n$ is one less than a multiple of $n$. Is there a version ...
Turbo's user avatar
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2 votes
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How to choose a prime p s.t. n-th cyclotomic polynomial splits into as much as possible irreducible polynomials while p is almost constant size?

The reason I ask this question is that cyclotomic polynomial is critical to the construction of lattice-based cryptography. In most of the existing lattice-based cryptographic schemes, $n$ is usually ...
user67451's user avatar
1 vote
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202 views

Prime generating polynomials

Continuation to this previous question. According to Lemke-Oliver, an irreducible polynomial $G$ of degree $g$ with positive leading coefficient and $\Gamma_G\neq0$ (with $\Gamma_G$ a certain factor ...
Delmastro's user avatar
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