Results 101 to 110 of about 2,595 (231)
On a Diophantine equation of Erdös
Proceedings of the Japan Academy, Series A, Mathematical Sciences, 1994 The second lemma is not proved in the quoted paper. It would lead to a polynomial bound in the height of the binary form. Despite this the main results can be true.
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A Diophantine equation appearing in Diophantine approximation
, 2001 All Diophantine equations ax2 + by2 + cz2 = 1 + dxyz, with a, b, c, d ∈ N and a|d, b|d, c|d, having solutions (x, y, z) ∈ N3 are determined. One particular equation of this type 2x2 + 2y2 + 3z2 = 1 + 6xyz appeared recently in connection with the ...
Schmidt, Asmus L., Jin, Yuan
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On the exponential Diophantine equation related to powers of two consecutive terms of Lucas sequences. [PDF]
Ramanujan J, 2021 Ddamulira M, Luca F.
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Diophantine equation $\frac{q^n-1}{q-1}=y$ for four prime divisors of $y-1$
, 2005 summary:In this paper the special diophantine equation $\frac{q^{n}-1}{q-1}=y$ with integer coefficients is discussed and integer solutions are sought. This equation is solved completely just for four prime divisors of $y-1$
Polický, Zdeněk
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On the Diophantine Equation x2 – kxy + ky2 + ly = 0, l = 2n
Annals of the West University of Timisoara: Mathematics and Computer Science, 2017 We consider the Diophantine equation x2-kxy+ky2+ ly = 0 for l = 2n and determine for which values of the odd integer k, it has a positive integer solution x and y.
Mavecha Sukrawan
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THE POWERS IN THE SMARANDACHE CUBIC PRODUCT SEQUENCES [PDF]
, 2000 Let P and Q denote the Smarandache cubic product sequences of the first kind and the second kind respectively.
Maohua, Le
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On Diophantine equations involving Lucas sequences
Open Mathematics, 2019 In this paper, we shall study the Diophantine equation un = R(m)P(m)Q(m), where un is a Lucas sequence and R, P and Q are polynomials (under weak assumptions).
Trojovský Pavel
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A radical diophantine equation
, 1981 All solutions in positive integers x, y z of the diophantine equation x1m + y1n = z1r are determined, where m, n, r are given positive integers. The proof makes use of a simple criterion for the irreducibility of the polynomial xn − a over the rationals,
Newman, Morris
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On the Diophantine equation $\frac{q^n-1}{q-1}=y$
, 2003 summary:There exist many results about the Diophantine equation $(q^n-1)/(q-1)=y^m$, where $m\ge 2$ and $n\geq 3$. In this paper, we suppose that $m=1$, $n$ is an odd integer and $q$ a power of a prime number.
Khosravi, Amir, Khosravi, Behrooz
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Solutions of the diophantine equation ... [PDF]
, 2011 In this paper, we study the diophantine equation 2 x + p y = z 2 where where p is a prime number and x, y and z are non-negative ...
Alongkot Suvarnamani
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