AbstractLetFbe a number field, Supposex,y∈F* have the property that for alln∈Zand almost all prime ideals p of the ring of integers ofF* one has thatyn≡1 (modp) wheneverxn≡1 (modp). We show that thenyis a power ofx. This answers a question of Erdős. We also prove an elliptic analogue of this result
AbstractLet P be a prime ideal in the ring of integers R of a number field F, with P∩Z=pZ, and assum...
We study a problem on specializations of multiples of rational points on elliptic curves analogous t...
Let Q ̄ be an algebraic closure of Q, and for any prime number p, denote by Q(µp) the cyclotomic sub...
AbstractLetFbe a number field, Supposex,y∈F* have the property that for alln∈Zand almost all prime i...
AbstractLet p be a prime number. We say that a number field F satisfies the condition (Hp′) when for...
AbstractIf lr(p) is the least positive integral value of x for which y2 ≡ x(x + 1) ⋯ (x + r − 1)(mod...
AbstractLetkbe a number field and denote by okits ring of integers. Let p be a non-zero prime ideal ...
AbstractLet A be an abelian variety over a number field K. If P and Q are K-rational points of A suc...
Let R be a Noetherian ring and I an ideal in R. Then there exists an integer k such that for all n ≥...
AbstractLet E/Q be an elliptic curve. For a prime p of good reduction, let E(Fp) be the set of ratio...
The orders of the reductions of a point in the Mordell–Weil group of an elliptic curve by J. Cheon a...
The dissertation consists of four chapters. The first chapter is an introduction, where we formulate...
If A/K is an abelian variety over a number field and P and Q are rational points, the original suppo...
AbstractLet ∞ be a fixed place of a global function field k. Let E be an elliptic curve defined over...
Given an elliptic curve E and a positive integer N, we consider the problem of counting the number o...
AbstractLet P be a prime ideal in the ring of integers R of a number field F, with P∩Z=pZ, and assum...
We study a problem on specializations of multiples of rational points on elliptic curves analogous t...
Let Q ̄ be an algebraic closure of Q, and for any prime number p, denote by Q(µp) the cyclotomic sub...
AbstractLetFbe a number field, Supposex,y∈F* have the property that for alln∈Zand almost all prime i...
AbstractLet p be a prime number. We say that a number field F satisfies the condition (Hp′) when for...
AbstractIf lr(p) is the least positive integral value of x for which y2 ≡ x(x + 1) ⋯ (x + r − 1)(mod...
AbstractLetkbe a number field and denote by okits ring of integers. Let p be a non-zero prime ideal ...
AbstractLet A be an abelian variety over a number field K. If P and Q are K-rational points of A suc...
Let R be a Noetherian ring and I an ideal in R. Then there exists an integer k such that for all n ≥...
AbstractLet E/Q be an elliptic curve. For a prime p of good reduction, let E(Fp) be the set of ratio...
The orders of the reductions of a point in the Mordell–Weil group of an elliptic curve by J. Cheon a...
The dissertation consists of four chapters. The first chapter is an introduction, where we formulate...
If A/K is an abelian variety over a number field and P and Q are rational points, the original suppo...
AbstractLet ∞ be a fixed place of a global function field k. Let E be an elliptic curve defined over...
Given an elliptic curve E and a positive integer N, we consider the problem of counting the number o...
AbstractLet P be a prime ideal in the ring of integers R of a number field F, with P∩Z=pZ, and assum...
We study a problem on specializations of multiples of rational points on elliptic curves analogous t...
Let Q ̄ be an algebraic closure of Q, and for any prime number p, denote by Q(µp) the cyclotomic sub...
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