22 citations · 35 across the 8 of their papers we have counts for
9 papers
Apollonius circles and the number of irreducible factors of polynomials
Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Yann Bugeaud +2
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 ,…
A kit for linear forms in three logarithms
Maurice Mignotte, Paul Voutier
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 bound…
There is no Diophantine --quadruple
Nicolae Ciprian Bonciocat, Mihai Cipu, Maurice Mignotte
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 --set. Such objects are usually s…
Two-parameter families of uniquely extendable Diophantine triples
Mihai Cipu, Yasutsugu Fujita, Maurice Mignotte
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…
Elementary Trigonometric Sums related to Quadratic Residues
A. Laradji, M. Mignotte, N. Tzanakis
Let p be a prime = 3 (mod 4). A number of elegant number-theoretical properties of the sums T(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} tan(n^2π/p) and C(p) = \sqrt{p}sum_{n=1}^{(p-1)/2} co…
On a conjecture on exponential Diophantine equations
Mihai Cipu, Maurice Mignotte
We study the solutions of a Diophantine equation of the form , where , and . The main result is that if there ex…