关于Diophantine方程(n+1)+(n+2)y=nz

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).     

On the Global Character of the Difference Equation X n + 1 =

We investigate the global stability, the periodic character, and the boundedness nature of solutions of the difference equation x n +1 = f + n x n m (2 k +1) + i x n m 2 l A + x n m 2 l , n =0,1,… where k and l are non-negative integers, the parameters f , n , i , A are non-negative real numbers with f + n + i >0, and the initial conditions are non-negative real numbers. We show that the solutions exhibit a trichotomy character depending upon the parameters n , i and A .     

关于函数方程f1n1+af1m1f2m2+f2n2=1

对于函数方程f1n1+af1m1f2m2+f2n2=1,其中a∈C/{0},n1,n2,m1,m2∈N,给出存在非常数亚纯函数解和整函数解的必要条件.     

Effective primality tests for integers of the formsN=k3 n +1 andN=k2 m 3 n +1

Using third roots of unity Proth's theorem for primality testing is generalized to integers of the formN=k3 ⁿ +1, avoiding the use of Lucas sequences which are more suitable ifN+1 is factored instead ofN–1. This approach has the advantage of being easily combined with Proth's test and gives polynomial time algorithms for testing integers of the formN=k2 ^m 3 ⁿ +1.     

On the diophantine equationD 1 x 2+D 2 m =4y n

For anyD ₁,D ₂, leth(-D ₁ D ₂) denote the class number of the imaginary quadratic field . In this paper we prove that the equationD ₁ x ²+D ₂ ^m =4y ⁿ.D ₁,D ₂,x, y, m, n, gcd (D ₁x,D ₂y=1,2m,n an odd prime,nh(-D ₁ D ₂, has only a finite number of solutions (D ₁,D ₂,x,y,m,n) withn>5. Moreover, the solutions satisfy 4y ⁿ相似文献   

关于丢番图方程x￣2+D=y￣n

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     

关于丢番图方程x￣2+D=y￣n

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     

A ternary Diophantine inequality by primes with one of the form $$p=x^2+y^2+1$$ p = x 2 + y 2 + 1

The Ramanujan Journal - In this paper we solve the ternary Piatetski-Shapiro inequality with prime numbers of a special form. More precisely we show that, for any fixed $$1<\frac{427}{400}$$...     

关于方程xy+yz+zx=n的正整数解

本文在广义Ｒｉｅｍａｎｎ猜想成立的条件下证明了：当且仅当正整数ｎ＝１，２，４，６，１０，１８，２２，３０，４２，５８，７０，７８，１０２，１３０，１９０，２１０，３３０，４６２时，方程ｘｙ＋ｙｚ＋ｚｘ＝ｎ无正整数解（ｘ，ｙ，ｚ）．     

方程xy+yz+zx=n的正整数解

本文用 Ｓｉｅｇｅｌ－Ｔａｔｕｚａｗａ定理证明了：当ｎ＞１．２×１０~１１时,至多有两个正 整数ｎ。使方程ｘｕ＋ｙｚ＋ｚｘ＝ｎ无适合（ｘ,ｙ,ｚ）＝１且０＜ｘ＜ｙ＜ｚ的解（ｘ,ｙ,ｚ）, 并给出类数为２的二次域与多项式表素数的一个结果．     

On a class of transitive permutation groups of prime degreep=4n+1

SupposeG is a nonsolvable transitive permutation group of prime degreep, such that |N _G v(P)|=p(p−1) for some Sylowp-subgroupP ofG. Letq be a generator of the subgroup ofN _G (P), fixing one letter (it is easy to show that this subgroup is cyclic). Assume thatG contains an elementj such thatj ⁻¹ qj=q ^(p+1)/2. We shall prove that for almost all primesp of the formp=4n+1, a group that satisfies the above conditions must be the symmetric group on a set withp elements.     

On the recursive sequencex_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}

The boundedness, global attractivity, oscillatory and asymptotic periodicity of the positive solutions of the difference equation of the form $$x_{n + 1} = \alpha + \frac{{x_{n - 1}^p }}{{x_n^p }}, n = 0,1,...$$ is investigated, where all the coefficients are nonnegative real numbers.     

On the difference equationx_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - 1}^p }}

We study, firstly, the dynamics of the difference equation $x_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - 1}^p }}$ , withp ∈ (0,1) and α∈ [0, ∞). Then, we generalize our results to the (k + 1)th order difference equation $x_{n + 1} = \alpha + \frac{{x_n^p }}{{x_{n - k}^p }}$ ,k = 2, 3,... with positive initial conditions.     

差分方程xn+1=xn+xαn/nβ解的渐近性

我们研究差分方程(1)的解的渐近性和全局吸引性.     

On the matrix equations AH + HA1 = A1H + HA = I

This paper considers the simultaneous solution of the matrix equations AH + HA¹ = A¹H + HA = I, where H is Hermitian. A full characterization of A in terms of a given H is obtained. Various results are also obtained for those H satisfying the equations with a given A.