Polynomial products modulo primes and applications
From MaRDI portal
Publication:2297587
DOI10.1007/s00605-019-01359-6zbMath1446.11030arXiv1810.06310OpenAlexW2996882382WikidataQ126411838 ScholiaQ126411838MaRDI QIDQ2297587
Publication date: 20 February 2020
Published in: Monatshefte für Mathematik (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1810.06310
polynomialsperfect powersDiophantine equationsdistribution of sequences modulo \(p\)dynamical system modulo \(p\)prime ideals of number fields
Quadratic extensions (11R11) Counting solutions of Diophantine equations (11D45) Distribution of prime ideals (11R44) Polynomials (irreducibility, etc.) (11R09) Sequences (mod (m)) (11B50)
Cites Work
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Unnamed Item
- Powerful numbers in \((1^k +1)(2^k+1) \cdots (n^k +1)\)
- A note on \(n!\) modulo \(p\)
- Irreducibility criteria of Schur-type and Pólya-type
- Sur un problème de M. Erdős
- On squares in polynomial products
- Sur une question d'Erdős et Schinzel. II. (On a question of Erdős and Schinzel. II)
- Squares in \((1^2+1)\dots(n^2+1)\)
- A note on the products \((1^\mu +1)(2^\mu +1)\dots (n^\mu +1)\)
- The product of consecutive integers is never a power
- Some effective cases of the Brauer-Siegel theorem
- Distribution of factorials modulo \(p\)
- Powers in \(\prod_{k=1}^n (ak^{2^l\cdot3^m}+b)\)
- On the products \((1^\ell +1)(2^\ell +1)\cdots (n^\ell +1)\)
- Permutations in Abelian groups and the sequence \(n!\pmod p\).
- Dynamical systems of non-algebraic origin: Fixed points and orbit lengths
- Perfect powers from products of consecutive terms in arithmetic progression
- Squares in (12 + m 2) ⋯ (n 2 + m 2)
- Neither (4k 2 + 1) nor (2k(k – 1) + 1) is a Perfect Square
- On the diophantine equation $n(n+1)...(n+k-1) = bx^l$
- On the Diophantine Equation n(n + d) · · · (n + (k − 1)d) = byl
- The equation n(n+d) ⋅⋅⋅(n+(k-1)d)=by2with ω(d)≤6 or d≤1010
- Criteria for the irreducibility of polynomials