Integral points and arithmetic progressions on Huff curves
نویسندگان
چکیده
منابع مشابه
Arithmetic progressions on Huff curves
We look at arithmetic progressions on elliptic curves known as Huff curves. By an arithmetic progression on an elliptic curve, we mean that either the x or y-coordinates of a sequence of rational points on the curve form an arithmetic progression. Previous work has found arithmetic progressions on Weierstrass curves, quartic curves, Edwards curves, and genus 2 curves. We find an infinite number...
متن کاملArithmetic Progressions on Edwards Curves
Several authors have investigated the problem of finding elliptic curves over Q that contain rational points whose x-coordinates are in arithmetic progression. Traditionally, the elliptic curve has been taken in the form of an elliptic cubic or elliptic quartic. Moody studied this question for elliptic curves in Edwards form, and showed that there are infinitely many such curves upon which ther...
متن کاملOn Arithmetic Progressions on Genus Two Curves
We study arithmetic progression in the x-coordinate of rational points on genus two curves. As we know, there are two models for the curve C of genus two: C : y = f5(x) or C : y = f6(x), where f5, f6 ∈ Q[x], deg f5 = 5, deg f6 = 6 and the polynomials f5, f6 do not have multiple roots. First we prove that there exists an infinite family of curves of the form y = f(x), where f ∈ Q[x] and deg f = ...
متن کاملOn Simultaneous Arithmetic Progressions on Elliptic Curves
and we consider two equations related by such a change of variables to represent the same curve (equivalently, we will deal with elliptic curves up to so-called Weierstrass changes of variables). Consider P0, . . . , Pn ∈ E(K), with Pi = (xi, yi) such that x0, . . . , xn is an arithmetic progression. We say that P0, . . . , Pn are in x-arithmetic progression (x-a.p.) and also say that E has an ...
متن کاملOn arithmetic progressions on Edwards curves
Let be m ∈ Z>0 and a, q ∈ Q. Denote by APm(a, q) the set of rational numbers d such that a, a + q, . . . , a + (m − 1)q form an arithmetic progression in the Edwards curve Ed : x2 +y2 = 1+d x2y2. We study the set APm(a, q) and we parametrize it by the rational points of an algebraic curve.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Publicationes Mathematicae Debrecen
سال: 2018
ISSN: 0033-3883
DOI: 10.5486/pmd.2018.8018