Displaying similar documents to “On power residue characters of units and the representation of numbers by quadratic forms”

On the computation of quadratic 2 -class groups

Wieb Bosma, Peter Stevenhagen (1996)

Journal de théorie des nombres de Bordeaux

Similarity:

We describe an algorithm due to Gauss, Shanks and Lagarias that, given a non-square integer D 0 , 1 mod 4 and the factorization of D , computes the structure of the 2 -Sylow subgroup of the class group of the quadratic order of discriminant D in random polynomial time in log D .

Prime factors of values of polynomials

J. Browkin, A. Schinzel (2011)

Colloquium Mathematicae

Similarity:

We prove that for every quadratic binomial f(x) = rx² + s ∈ ℤ[x] there are pairs ⟨a,b⟩ ∈ ℕ² such that a ≠ b, f(a) and f(b) have the same prime factors and min{a,b} is arbitrarily large. We prove the same result for every monic quadratic trinomial over ℤ.