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 作者：Nobuhiro Terai , Takeshi Hibino 来源：[J].Periodica Mathematica Hungarica(IF 0.261), 2017, Vol.74 (2), pp.227-234 摘要：...\) Then we show that the exponential Diophantine equation $$(3pm^2-1)^x+(p(p-3)m^2+1)^y=(pm)^z$$ has only the positive integer solution $$(x, y, z)=(1, 1, 2)$$ under some conditions. As a corollary, we derive that the exponential Diophantine equation $$(15m^2-1)^x+(10m^2+1)^...  作者：Eva G. Goedhart , Helen G. Grundman 来源：[J].Periodica Mathematica Hungarica(IF 0.261), 2017, Vol.75 (2), pp.196-200 摘要：We prove that for each prime p , positive integer \(\alpha$$ , and non-negative integers $$\beta$$ and $$\gamma$$ , the Diophantine equation $$X^{2N} + 2^{2\alpha }5^{2\beta }{p}^{2\gamma } = Z^5$$ has no solution with N , X , $$Z\in \mathbb {Z}^+$$ , $$N > 1$$ , and $$\gcd (X...  作者：Ruiqin Fu , Hai Yang 来源：[J].Periodica Mathematica Hungarica(IF 0.261), 2017, Vol.75 (2), pp.143-149 摘要：... In this paper we prove that if \(c\mid m$$ and $$m>36c^3 \log c$$ , then the equation $$(am^2+1)^x+(bm^2-1)^y=(cm)^z$$ has only the positive integer solution $$(x,\ y,\ z)$$ = $$(1,\ 1,\ 2)$$ .
 作者：Farzali Izadi , Mehdi Baghalaghdam 来源：[J].Periodica Mathematica Hungarica(IF 0.261), 2017, Vol.75 (2), pp.190-195 摘要：In this paper, we solve the simultaneous Diophantine equations $$m \cdot ( x_{1}^k+ x_{2}^k +\cdots + x_{t_1}^k)=n \cdot (y_{1}^k+ y_{2}^k +\cdots + y_{t_2}^k )$$ , $$k=1,3$$ , where $$t_1, t_2\ge 3$$ , and m , n are fixed arbitrary and relatively prime positive integers. This i...
 作者：Xiaoying Du 来源：[J].Czechoslovak Mathematical Journal(IF 0.3), 2017, Vol.67 (3), pp.645-653 摘要：For any positive integer D which is not a square, let ( u 1, v 1) be the least positive integer solution of the Pell equation u 2 − Dv 2 = 1, and let h (4 D ) denote the class number of binary quadratic primitive forms of discriminan...
 作者：Yong Zhang , Deyi Chen 来源：[J].Periodica Mathematica Hungarica(IF 0.261), 2020, Vol.80 (1), pp.138-144 摘要：... We give conditions for under which the Diophantine equation has infinitely many nontrivial integer solutions and prove that this equation has infinitely many rational parametric solutions for with nonzero integer . Moreover, we show that it has a rational parametric solution ...
 作者：H.R. Gallegos-Ruiz , N. Katsipis , Sz. Tengely ... 来源：[J].Journal of Number Theory(IF 0.466), 2020, Vol.208, pp.418-440 摘要：Abstract(#br)By finding all integral points on certain elliptic and hyperelliptic curves we completely solve the Diophantine equation ( n k ) = ( m l ) + d for − 3 ≤ d ≤ 3 and ( k , l ) ∈ { ( 2 , 3 ) , ( 2 , 4 ) , ...
 作者：Bahar Demirtürk Bitim 来源：[J].Periodica Mathematica Hungarica(IF 0.261), 2019, Vol.79 (2), pp.210-217 摘要：Abstract(#br)In this paper we find ( n , m , a ) solutions of the Diophantine equation $$L_{n}-L_{m}=2\cdot 3^{a}$$ L n - L m = 2 · 3 a , where $$L_{n}$$ L n and $$L_{m}$$ L m are Lucas numbers with $$a\ge 0$$ a ≥ 0 and $$n>m\ge 0$$ n > m ≥ 0 . For proving our theorem, w...
 作者：Maciej Gawron , Maciej Ulas 来源：[J].Journal of Number Theory(IF 0.466), 2016, Vol.159, pp.101-122 摘要：Abstract(#br)In this paper we investigate Diophantine equations of the form T 2 = G ( X ‾ ) , X ‾ = ( X 1 , … , X m ) , where m = 3 or m = 4 and G is a specific homogeneous quintic form. First, we prove that if F ( x , y , z ) = x 2 + y 2 + a z 2 ...
 作者：Yong Zhang , Tianxin Cai 来源：[J].Periodica Mathematica Hungarica(IF 0.261), 2015, Vol.70 (2), pp.209-215 摘要：... We consider the Diophantine equation $$f(x)f(y)=f(z^2)$$ . For two classes of irreducible quadratic polynomials, this equation has infinitely many nontrivial integer solutions, if the corresponding Pell’s equations satisfy a condition. For a special cubic polynomial, i...