منابع مشابه
On the Sum-Product Problem on Elliptic Curves
Let E be an ordinary elliptic curve over a finite field IF q of q elements and x(Q) denote the x-coordinate of a point Q = (x(Q), y(Q)) on E. Given an IF q-rational point P of order T , we show that for any subsets A, B of the unit group of the residue ring modulo T , at least one of the sets {x(aP) + x(bP) : a ∈ A, b ∈ B} and {x(abP) : a ∈ A, b ∈ B} is large. This question is motivated by a se...
متن کاملOn the elliptic curve analogue of the sum-product problem
Let E be an elliptic curve over a finite field Fq of q elements and x(P ) to denote the x-coordinate of a point P = (x(P ), y(P )) ∈ E. Let ⊕ denote the group operation in the Abelian group E(Fq) of Fq -rational points on E. We show that for any sets R,S ⊆ E(Fq) at least one of the sets { x(R)+ x(S): R ∈R, S ∈ S} and {x(R⊕ S): R ∈R, S ∈ S} is large. This question is motivated by a series of rec...
متن کاملThe Erdős - Szemerédi problem on sum set and product set
The basic theme of this paper is the fact that if A is a finite set of integers, then the sum and product sets cannot both be small. A precise formulation of this fact is Conjecture 1 below due to Erdős-Szemerédi [E-S]. (see also [El], [T], and [K-T] for related aspects.) Only much weaker results or very special cases of this conjecture are presently known. One approach consists of assuming the...
متن کاملErdős-szemerédi Problem on Sum Set and Product Set
The basic theme of this paper is the fact that if A is a finite set of integers, then the sum and product sets cannot both be small. A precise formulation of this fact is Conjecture 1 below due to Erdős-Szemerédi [E-S]. (see also [El], [T], and [K-T] for related aspects.) Only much weaker results or very special cases of this conjecture are presently known. One approach consists of assuming the...
متن کاملAn Algorithm to Solve the Equal-Sum-Product Problem
A recursive algorithm is constructed which finds all solutions to a class of Diophantine equations connected to the problem of determining ordered n-tuples of positive integers satisfying the property that their sum is equal to their product. An examination of the use of Binary Search Trees in implementing the algorithm into a working program is given. In addition an application of the algorith...
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ژورنال
عنوان ژورنال: SIAM Journal on Discrete Mathematics
سال: 2015
ISSN: 0895-4801,1095-7146
DOI: 10.1137/140952004