منابع مشابه
ON THE DIOPHANTINE EQUATION Ax2+22m =yn
Let h denote the class number of the quadratic field Q( √−A) for a square free odd integer A> 1, and suppose that n> 2 is an odd integer with (n,h)= 1 and m> 1. In this paper, it is proved that the equation of the title has no solution in positive integers x and y if n has any prime factor congruent to 1 modulo 4. If n has no such factor it is proved that there exists at most one solution with ...
متن کاملTHE DIOPHANTINE EQUATION x2+2k =yn, II
New results regarding the full solution of the diophantine equationx2+2k=yn in positive integers are obtained. These support a previous conjecture, without providing a complete proof.
متن کاملOn the Diophantine Equation x 2 + 2 α 5 β 13 γ = yn
In this paper, we find all the solutions of the Diophantine equation x + 2 513 = y in nonnegative integers x, y, α, β, γ, n ≥ 3 with x and y coprime. In fact, for n = 3, 4, 6, 8, 12, we transform the above equation into several elliptic equations written in cubic or quartic models for which we determine all their {2, 5, 13}-integer points. For n ≥ 5, we apply a method that uses primitive diviso...
متن کاملON THE DIOPHANTINE EQUATION x m − 1 x − 1 = yn − 1 y − 1
There is no restriction in assuming that y > x in (1) and thus we have m > n. This equation asks for integers having all their digits equal to one with respect to two distinct bases and we still do not know whether or not it has finitely many solutions. Even if we fix one of the four variables, it remains an open question to prove that (1) has finitely many solutions. However, when either the b...
متن کاملThe global attractivity of the rational difference equation yn = (yn-k + yn-m) / (1 + yn-k yn-m)
This paper studies global asymptotic stability for positive solutions to the equation yn = yn−k + yn−m 1 + yn−k yn−m , n = 0, 1, . . . , with y−m , y−m+1, . . . , y−1 ∈ (0,∞) and 1 ≤ k < m. The paper includes a discussion of stability for a wide class of symmetric rational difference equations which includes the type studied here as well as several other in the recent literature. c © 2006 Elsev...
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ژورنال
عنوان ژورنال: Glasgow Mathematical Journal
سال: 1993
ISSN: 0017-0895,1469-509X
DOI: 10.1017/s0017089500009757