共查询到20条相似文献,搜索用时 0 毫秒
1.
S. Sh. Kozhegel’dinov 《Mathematical Notes》2011,89(3-4):349-360
We study the set of all natural solutions of the equation x 4 + y 2 = z 2, obtain general formulas describing all such solutions, and prove their equivalence. 相似文献
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Let n be a positive integer. In this paper, using the results on the existence of primitive divisors of Lucas numbers and some properties of quadratic and exponential diophantine equations, we prove that if n ≡ 3 (mod 6), then the equation x 2 + (3n 2 + 1) y = (4n 2 + 1) z has only the positive integer solutions (x, y, z) = (n, 1, 1) and (8n 3 + 3n, 1, 3). 相似文献
4.
Andrew Bremner 《manuscripta mathematica》1989,65(4):479-487
We determine all cubic number fields such that the title equation has a solution in the ring of integers of the field.I am grateful to H. M. Edgar for suggesting this problem. 相似文献
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Maohua Le 《Czechoslovak Mathematical Journal》2006,56(4):1109-1116
Let a, b, c, r be positive integers such that a
2 + b
2 = c
r
, min(a, b, c, r) > 1, gcd(a, b) = 1, a is even and r is odd. In this paper we prove that if b ≡ 3 (mod 4) and either b or c is an odd prime power, then the equation x
2 + b
y
= c
z
has only the positive integer solution (x, y, z) = (a, 2, r) with min(y, z) > 1. 相似文献
7.
K. P. Chinda 《Aequationes Mathematicae》1974,11(2-3):196-198
8.
本文对不定方程x2+y2=z2给出了四个推广,并用一种统一的解法对这四个推广给出了解答. 相似文献
9.
A. G. Kisun'ko 《Mathematical Notes》1971,10(4):667-671
Equality of distributions is shown of even and odd values of the order of the zero at the point s=1 of L-functions of elliptic curves x3+y3=D, where D is a positive integer not divisible by a cube.Translated from Matematicheskie Zametki, Vol. 10, No. 4, pp. 407–414, October, 1971. 相似文献
10.
Wang Xiaoying 《Periodica Mathematica Hungarica》2013,66(2):193-200
For any fixed positive integer D which is not a square, let (u, υ) = (u 1, υ 1) be the fundamental solution of the Pell equation u 2 ? Dυ 2 = 1. Further let $\mathbb{D}$ be the set of all positive integers D such that D is odd, D is not a square and gcd(D, υ 1) > max(1, √D/8). In this paper we prove that if (x, y, z) is a positive integer solution of the equation x y + y x = z 2 satisfying gcd(x, y) = 1 and xy is odd, then either $x \in \mathbb{D}$ or $y \in \mathbb{D}$ . 相似文献
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I. Fenyő 《Acta Mathematica Hungarica》1970,21(1-2):35-46
Ohne ZusammenfassungHerrn ProfessorG. Alexits zum 70. Geburtstag gewidmet 相似文献
14.
使用代数数论和p-adic分析,我们找到了椭圆曲线y^2=x^3+27x-62上所有的整数点.我们给出了一个全虚四次域的子环上计算基本单位和二次代数数“不相关分解”的方法. 相似文献
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关于不定方程组x-1=3py^2,x^2+x+1=3z^2 总被引:2,自引:0,他引:2
设P为素数,利用同余及高次丢番图方程的一些结果证明了不定方程组x-1=3py^2,x^2+x+1=3z^2仅有正整数解(p,x,y,z)=(7,22,1,13)。 相似文献
17.
L. Makar-Limanov 《Israel Journal of Mathematics》1996,96(2):419-429
In this note it will be proved that the threefold in ?4 which is given byx+x 2 y+z 2+t 3=0 is not isomorphic to ?3. Here ? is the field of complex numbers. 相似文献
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Integral solutions toy
2=x
3+k, where either thex's or they's, or both, are in arithmetic progression are studied. When both thex's and they's are in arithmetic progression, then this situation is completely solved. One set of solutions where they's formed an arithmetic progression of length 4 had already been constructed. In this paper, we construct infinitely many
sets of solutions where there are 4x's in arithmetic progression and we disprove Mohanty's Conjecture [8] by constructing infinitely many sets of solutions where
there are 4, 5 and 6y's in arithmetic progression. 相似文献