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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...

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