22 citations · 40 across the 5 of their papers we have counts for
8 papers
On the Hilbert depth of the quotient ring of the edge ideal of a star graph
Silviu Balanescu, Mircea Cimpoeas, Mihai Cipu
Let and be the edge ideal of star graph. We prove that $\operatorname{hdepth}(S_n/I_n)\geq \left\lceil \frac{n}{2…
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 ,…
Apollonius circles and irreducibility criteria for polynomials
Anca Iuliana Bonciocat, Nicolae Ciprian Bonciocat, Yann Bugeaud +1
We prove the irreducibility of integer polynomials whose roots lie inside an Apollonius circle associated to two points on the real axis with integer abscisae and , w…
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…
Searching for Diophantine quintuples
Mihai Cipu, Tim Trudgian
We consider Diophantine quintuples . These are sets of distinct positive integers, the product of any two elements of which is one less than a perfect square. It…
On the Behaviour of Stanley Depth under Variable Adjunction
Mihai Cipu, Muhammad Imran Qureshi
Let be a polynomial ring in variables over the field . For integers consider the ideal in . In thi…
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…