Pseudoprimes and a generalization of Artin's conjecture

Samuel Wagstaff

Displaying similar documents to “Pseudoprimes and a generalization of Artin's conjecture”

On character sums and the non-vanishing for s > 0 of Dirichlet L-series belonging to real odd characters χ

S. Chowla, I. Kessler, M. Livingston (1977)

Acta Arithmetica

Similarity:

Γ*(8)

J. Bovey (1974)

Acta Arithmetica

Similarity:

The ternary Goldbach problem in arithmetic progressions

Jianya Liu, Tao Zhan (1997)

Acta Arithmetica

Similarity:

For a large odd integer N and a positive integer r, define b = (b₁,b₂,b₃) and $(N, r) = b \in ℕ ³ : 1 \leq b_{j} \leq r, (b_{j}, r) = 1 a n d b ₁ + b ₂ + b ₃ \equiv N (m o d r) .$ It is known that $(N, r) = r ² \prod_{p | r} p | N ((p - 1) (p - 2) / p ²) \prod_{p | r} p ∤ N ((p ² - 3 p + 3) / p ²)$ . Let ε > 0 be arbitrary and $R = N^{1 / 8 - ε}$ . We prove that for all positive integers r ≤ R, with at most $O (R l o g^{- A} N)$ exceptions, the Diophantine equation ⎧N = p₁+p₂+p₃, ⎨ $p_{j} \equiv b_{j} (m o d r),$ j = 1,2,3,⎩ with prime variables is solvable whenever b ∈ (N,r), where A > 0 is arbitrary.