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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
2.
尚旭 《纯粹数学与应用数学》2017,33(4)
在高斯整环中,利用代数数论与同余理论的方法,讨论了不定方程x~2+4~n=y~(13)(n=4,5,6)的整数解问题,得出了当n=4,5时无整数解;n=6是仅有整数解(x,y)=(64,2)和(x,y)=(-64,2)的结论,推进了不定方程整数解的研究. 相似文献
3.
Liqun Tao 《The Ramanujan Journal》2009,19(3):325-338
In this paper we consider the Diophantine equation x
2+5
m
=y
n
, n>2, m>0. We prove that the equation has no positive integer solutions when 2∤
m, nor when 2∣m under the additional condition (x,y)=1, with the help of Bilu, Hanrot, and Voutier’s deep result in (J. Reine Angew. Math. 539:75–122, 2001).
Supported by the 973 Grant of P.R.C and SRFDP 20040284018. 相似文献
4.
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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Acta Mathematica Hungarica - Let n be a positive integer. We show that if the equation $$(1) \qquad \qquad \qquad x^4+2^ny^4=z^4$$ has a solution (x,y,z) in a cubic number field K with $$xyz \neq... 相似文献
7.
运用同余及元素阶的性质,证明了对任意的正整数n,丢番图方程(195n)x+(28n)y=(197n)z仅有正整数解(x, y, z)=(2,2,2)。 相似文献
8.
本文运用Baker方法证明了:当D=67时,方程x2+D=yn,x,y,n∈N,n>2,仅有解(x,y,n)=(110,23,3);当D=43或163时,该方程无解 相似文献
9.
本文运用Baker方法证明了:当D=67时,方程x2+D=yn,x,y,n∈N,n>2,仅有解(x,y,n)=(110,23,3);当D=43或163时,该方程无解 相似文献
10.
11.
关于Diophantine方程x3+1=py2 总被引:1,自引:0,他引:1
在素数p=3(8t+4)(8t+5)+1和p=3(8t+3)(8t+4)+1的情形下,运用初等数论的方法给出了丢番图方程x3+1=py2无正整数解的充分条件,并得到无数个6k+1型的素数p使得方程x3+1=py2无正整数解. 相似文献
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13.
Periodica Mathematica Hungarica - In this paper we find all positive integer solutions (x, y, n, a, b) of the equation in the title for non negative integers a... 相似文献
14.
设n是正整数.本文证明了:方程(n+1)+(n+2)y=nz仅当n=3时有正整数解(y,z)=(1,2). 相似文献
15.
在Jeismanowicz猜想的基础上,利用初等方法证明了对任意的正整数n, Diophantine方程(44n)x+(117n)y=(125n)z 仅有正整数解(x, y, z)=(2,2,2)。 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
19.
Giovanni Sansone 《Annali di Matematica Pura ed Applicata》1976,111(1):125-151
Sunto Nel 1969 A. Baker e H. Davenport hanno dimostrato che il sistema3x
2
−2=y
2
,8x
2
−7=z
2
ha soltanto le soluzioni |x|=|y|=|z|=1; |x|=11, |y|=19, |z|=31. Una seconda dimostrazione di P. Kanagasabapathy — Tharmambikai Ponmudurai è apparsa nell'ottobre 1975. L'A. dà una terza
dimostrazione che consente, con l'uso dei metodi classici dell'aritmetica, di controllare i ragionamenti in ogni punto.
A Dario Graffi nel suo 70° compleanno
Entrata in Redazione il 26 novembre 1975. 相似文献
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