On some classes of homogeneous ternary cubic diophantine equations
نویسندگان
چکیده
منابع مشابه
On Some Diophantine Equations (i)
In this paper we study the equation m−n = py,where p is a prime natural number, p≥ 3. Using the above result, we study the equations x + 6pxy + py = z and the equations ck(x 4 + 6pxy + py) + 4pdk(x y + pxy) = z, where the prime number p ∈ {3, 7, 11, 19} and (ck, dk) is a solution of the Pell equation, either of the form c −pd = 1 or of the form c − pd = −1. I. Preliminaries. We recall some nece...
متن کاملOn Some Diophantine Equations (iii)
In this paper we study the Diophantine equations ck(f +42fg+49g) + 28dk(f g + 7fg) = m, where (ck, dk) are solutions of the Pell equation c 2−7d2= 1.
متن کاملOn Some Diophantine Equations (ii)
In [7] we have studied the equation m − n = py, where p is a prime natural number p ≥ 3. Using the above result, in this paper, we study the equations ck(x 4 + 6px y +py) + 4pdk(x y + pxy) = 32z with p ∈ {5, 13, 29, 37}, where (ck, dk) is a solution of the Pell equation ∣∣c2 − pd2∣∣ = 1.
متن کاملSome remarks on diophantine equations and diophantine approximation
We give many equivalent statements of Mahler’s generalization of the fundamental theorem of Thue. In particular, we show that the theorem of Thue–Mahler for degree 3 implies the theorem of Thue for arbitrary degree ≥ 3, and we relate it with a theorem of Siegel on the rational integral points on the projective line P(K) minus 3 points. Classification MSC 2010: 11D59; 11J87; 11D25
متن کاملSome ternary cubic two-weight codes
We study trace codes with defining set L, a subgroup of the multiplicative group of an extension of degree m of the alphabet ring F3+uF3+u 2 F3, with u 3 = 1. These codes are abelian, and their ternary images are quasi-cyclic of co-index three (a.k.a. cubic codes). Their Lee weight distributions are computed by using Gauss sums. These codes have three nonzero weights when m is singly-even and |...
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: Arkiv för Matematik
سال: 1975
ISSN: 0004-2080
DOI: 10.1007/bf02386196