منابع مشابه
The diophantine equation x3 3 + y3 + z 3 − 2xyz = 0
We will be presenting two theorems in this paper. The first theorem, which is a new result, is about the non-existence of integer solutions of the cubic diophantine equation. In the proof of this theorem we have used some known results from theory of binary cubic forms and the method of infinite descent, which are well understood in the purview of Elementary Number Theory(ENT). In the second th...
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We propose an efficient search algorithm to solve the equation x3 + y3 + 2z3 = n for a fixed value of n > 0. By parametrizing |z|, this algorithm obtains |x| and |y| (if they exist) by solving a quadratic equation derived from divisors of 2|z|3±n. Thanks to the use of several efficient numbertheoretic sieves, the new algorithm is much faster on average than previous straightforward algorithms. ...
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= c for some integers a, b, c with ab 6= 0, has only finitely many integer solutions. Stoll & Tichy proved more generally that if a, b, c ∈ Q and ab 6= 0, then for m > n ≥ 3, the above equation has only finitely many integral solutions x, y. Independently, Rakaczki established a more precise finiteness result on this binomial equation and extended this result to more general equations (see Acta...
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If a, b and n are positive integers with b ≥ a and n ≥ 3, then the equation of the title possesses at most one solution in positive integers x and y, with the possible exceptions of (a, b, n) satisfying b = a + 1, 2 ≤ a ≤ min{0.3n, 83} and 17 ≤ n ≤ 347. The proof of this result relies on a variety of diophantine approximation techniques including those of rational approximation to hypergeometri...
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ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 1972
ISSN: 0022-314X
DOI: 10.1016/0022-314x(72)90058-3