Add to ORKG91 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.In this dissertation, we study the Tarry-Escott problem and some related diophantine systems over Z and over some quadratic fields. We give infinitely many solutions of the Tarry-Escott problem over Zi of degrees 2, 3, 4, 5 and 7, none of which can be directly derived from solutions over Z . We show that there are infinitely many solutions of the Tarry-Escott problem of degree 2 over an infinite family of rings Zn . We also solve some diophantine equations which have no integral solutions over some quadratic fields. We partially solve a generalized form of the Tarry-Escott problem of degree 2.U of I OnlyRestricted to the U of I community idenfinitely during bat...
AbstractLet D>2 be a square-free integer and define a direct graph G(D) such that the vertices of th...
The diophantine equation sp2 + y sp3 = z sp5 eqno(1) as an infinite number of integer solutions wit...
A search bound for the smallest solution of a quadratic diophantine equation over number fields in a...
91 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.In this dissertation, we study...
The numbers 1, 2, and 6 have the same sum and same sum of squares as 0, 4, 5. These two sets are sol...
Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equation...
The purpose of this research paper is to gain a deeper understanding of a famous unsolved mathematic...
International audienceThis paper gives a complete four-parameter solution of the simultaneous diopha...
We consider the diophantine equation xp - x = yq - y, in integers (x, p, y, q). We prove that for gi...
International audienceThis paper is concerned with the system of simultaneous diophantine equations ...
In this thesis, we study two of the most important questions in Arithmetic geometry: that of the exi...
Let K be an algebraic number field, and let h(x)=x3+ax be a polynomial over K. We prove that there e...
The p-adic models of statistical mechanics require the investigation of the roots of polynomial equa...
Let K be a p-adic field (a finite extension of some Q_p) and let K(t) be the field of rational funct...
A Diophantine problem means to find all solutions of an equation or system of equations in integers,...
AbstractLet D>2 be a square-free integer and define a direct graph G(D) such that the vertices of th...
The diophantine equation sp2 + y sp3 = z sp5 eqno(1) as an infinite number of integer solutions wit...
A search bound for the smallest solution of a quadratic diophantine equation over number fields in a...
91 p.Thesis (Ph.D.)--University of Illinois at Urbana-Champaign, 2009.In this dissertation, we study...
The numbers 1, 2, and 6 have the same sum and same sum of squares as 0, 4, 5. These two sets are sol...
Let K be any quadratic field with O-K its ring of integers. We study the solutions of cubic equation...
The purpose of this research paper is to gain a deeper understanding of a famous unsolved mathematic...
International audienceThis paper gives a complete four-parameter solution of the simultaneous diopha...
We consider the diophantine equation xp - x = yq - y, in integers (x, p, y, q). We prove that for gi...
International audienceThis paper is concerned with the system of simultaneous diophantine equations ...
In this thesis, we study two of the most important questions in Arithmetic geometry: that of the exi...
Let K be an algebraic number field, and let h(x)=x3+ax be a polynomial over K. We prove that there e...
The p-adic models of statistical mechanics require the investigation of the roots of polynomial equa...
Let K be a p-adic field (a finite extension of some Q_p) and let K(t) be the field of rational funct...
A Diophantine problem means to find all solutions of an equation or system of equations in integers,...
AbstractLet D>2 be a square-free integer and define a direct graph G(D) such that the vertices of th...
The diophantine equation sp2 + y sp3 = z sp5 eqno(1) as an infinite number of integer solutions wit...
A search bound for the smallest solution of a quadratic diophantine equation over number fields in a...