OnS-integral solutions of the equationy m =f(x)

Brindza, Β.

doi:10.1007/bf01974110

Cited by 75 publications

(97 citation statements)

References 7 publications

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“…Our next lemma is a special case of a general theorem concerning the superelliptic equations proved by Brindza [5].…”

Section: Auxiliary Resultsmentioning

confidence: 93%

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A Diophantine Problem Concerning Polygonal numbers

Kim¹,

Park²

2013

Bull. Aust. Math. Soc.

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“…Our next lemma is a special case of a general theorem concerning the superelliptic equations proved by Brindza [5].…”

Section: Auxiliary Resultsmentioning

confidence: 93%

“…Further, for k = 2 and 3 ≤ m, n ≤ 12, m = 4, the solutions (x, y) to (2) are (m, n, x, y) = (3, 3, 8, 3), (3,5,49,5), (3,6,8,2), (3,9,288,8), (3,10, 9800, 42), (6,5,25,5), (7,4,6,3), (7,9,6,2), (8,3,9,5), (8,6,9,3), (9, 3, 2, 2), (9,3,49,13), (9,6,49,7), (9,12,18,3), (11,3,81,18), (12,3,25,…”

Section: Introduction and The Main Resultsmentioning

confidence: 99%

A Diophantine Problem Concerning Polygonal numbers

Kim¹,

Park²

2013

Bull. Aust. Math. Soc.

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“…We apply this with F(X) = G(X), which has d = 4 simple roots. From list (6), and the fact that |a 0 | 2|a|, one checks easily that K 56H 5 . Thus, and then by a simple inductive argument we derive…”

Section: F(h) E(h Hmentioning

confidence: 99%

“…Certainly, the bound of Theorem 5 can easily be improved by tightening up our argument and also via using more modern estimates on size of solutions of Diophantine equations (see, for example, [5,6] and the references therein, for such better explicit estimates).…”

Section: Commentsmentioning

confidence: 99%

On Stable Quadratic Polynomials

et al. 2012

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Abstract. We recall that a polynomial f (X) ∈ K[X] over a field K is called stable if all its iterates are irreducible over K. We show that almost all monic quadratic polynomials f (X) ∈ ‫[ޚ‬X] are stable over ‫.ޑ‬ We also show that the presence of squares in so-called critical orbits of a quadratic polynomial f (X) ∈ ‫[ޚ‬X] can be detected by a finite algorithm; this property is closely related to the stability of f (X). We also prove there are no stable quadratic polynomials over finite fields of characteristic 2 but they exist over some infinite fields of characteristic 2.

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“…In this paper we consider the diophantine equation (1) x(x + [6] proved that (1) with (L, M ) = (2, 3) implies that (x, y) = (2, 1) or (14,5). MacLeod and Barrodale [5] showed in 1970 that (1) has no solutions if (L, M ) = (2, 4), (2,6), (2,8), (2,12), (4,8) or (5,10) and admits only the solution (x, y) = (8, 1) if (L, M ) = (3,6). Two years later Boyd and Kisilevsky [1] proved that (x, y) = (2, 1), (4,2), (55,19) are the only solutions of (1) if (L, M ) = (3,4).…”

mentioning

confidence: 99%