On generating infinitely many solutions of the Diophantine equation $A\sp{6}+B\sp{6}+C\sp{6}=D\sp{6}+E\sp{6}+F\sp{6}$
نویسندگان
چکیده
منابع مشابه
Infinitely Many Solutions of Superlinear Elliptic Equation
and Applied Analysis 3 Lemma 6 (see [17]). Assume that |Ω| < ∞, 1 ≤ p, r ≤ ∞, f ∈ C(Ω×R), and |f(x, u)| ≤ c(1+|u|). Then for every
متن کاملInfinitely many solutions for a bi-nonlocal equation with sign-changing weight functions
In this paper, we investigate the existence of infinitely many solutions for a bi-nonlocal equation with sign-changing weight functions. We use some natural constraints and the Ljusternik-Schnirelman critical point theory on C1-manifolds, to prove our main results.
متن کاملInfinitely many solutions for a class of $p$-biharmonic equation in $mathbb{R}^N$
Using variational arguments, we prove the existence of infinitely many solutions to a class of $p$-biharmonic equation in $mathbb{R}^N$. The existence of nontrivial solution is established under a new set of hypotheses on the potential $V(x)$ and the weight functions $h_1(x), h_2(x)$.
متن کاملInfinitely many insolvable Diophantine equations II
Let f(X1, . . . , Xm) be a quadratic form in m variables X1, . . . , Xm with integer coefficients. Then it is well-known that the Diophantine equation f(X1, . . . , Xm) = 0 has a nontrivial solution in integers if and only if the equation has a nontrivial solution in real numbers and the congruence f(X1, . . . , Xm) ≡ 0 (mod N) has a nontrivial solution for every integer N > 1. Such a principle...
متن کاملOn the Solutions to the Diophantine Equation
In this paper we are concerned with a question that has already been answered, involving Fibonacci-type sequences and their characteristic numbers. We are only interested in primitive sequences iconsecutive pairs of terms have no common factors) and for these sequences we ask: What numbers can be the characteristic of a sequence, and given such a number, how many sequences have it? Thoro [1] ha...
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: Mathematics of Computation
سال: 1970
ISSN: 0025-5718
DOI: 10.1090/s0025-5718-1970-0271020-4