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pro vyhledávání: '"Mignotte, Maurice"'
Autor:
Bonciocat, Anca Iuliana, Bonciocat, Nicolae Ciprian, Bugeaud, Yann, Cipu, Mihai, Mignotte, Maurice
We provide upper bounds for the sum of the multiplicities of the non-constant irreducible factors that appear in the canonical decomposition of a polynomial $f(X)\in\mathbb{Z}[X]$, in case all the roots of $f$ lie inside an Apollonius circle associat
Externí odkaz:
http://arxiv.org/abs/2303.04033
Autor:
Mignotte, Maurice, Voutier, Paul
We provide a technique to obtain explicit bounds for problems that can be reduced to linear forms in three complex logarithms of algebraic numbers. This technique can produce bounds significantly better than general results on lower bounds for linear
Externí odkaz:
http://arxiv.org/abs/2205.08899
A set of positive integers with the property that the product of any two of them is the successor of a perfect square is called Diophantine $D(-1)$--set. Such objects are usually studied via a system of generalized Pell equations naturally attached t
Externí odkaz:
http://arxiv.org/abs/2010.09200
Let A,K be positive integers and u=-2,-1,1 or 2. The main contribution of the paper is a proof that each of the D(u^2)-triples {K,A^2K+2uA,(A+1)^2K+2u(A+1)} has unique extension to a D(u^2)-quadruple.
Comment: This paper has 20 pages and has bee
Comment: This paper has 20 pages and has bee
Externí odkaz:
http://arxiv.org/abs/1611.08646
Autor:
Mignotte, Maurice, Voutier, Paul
Publikováno v:
Mathematics of Computation; Jul2024, Vol. 93 Issue 348, p1903-1951, 49p
Publikováno v:
Math. Proc. Camb. Phil. Soc. 158 (2015) 305-329
Let $u_k$ be a Lucas sequence. A standard technique for determining the perfect powers in the sequence $u_k$ combines bounds coming from linear forms in logarithms with local information obtained via Frey curves and modularity. The key to this approa
Externí odkaz:
http://arxiv.org/abs/1408.1710
Publikováno v:
Research in Number Theory; 4/21/2024, Vol. 10 Issue 2, p1-23, 23p
Autor:
Cipu, Mihai, Mignotte, Maurice
We study the solutions of a Diophantine equation of the form $a^x+b^y=c^z$, where $a\equiv 2 \pmod 4$, $b\equiv 3 \pmod 4$ and $\gcd (a,b,c)=1$. The main result is that if there exists a solution $(x,y,z)=(2,2,r)$ with $r>1$ odd then this is the only
Externí odkaz:
http://arxiv.org/abs/0812.0495
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