On a Diophantine problem with two primes and s powers of two
Alessandro Languasco, Alessandro Zaccagnini (2010)
Acta Arithmetica
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Alessandro Languasco, Alessandro Zaccagnini (2010)
Acta Arithmetica
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R. Baker (1989)
Acta Arithmetica
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D. Eric Freeman (2003)
Acta Arithmetica
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Utz, W.R. (1982)
International Journal of Mathematics and Mathematical Sciences
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Alessandro Languasco, Valentina Settimi (2012)
Acta Arithmetica
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S. Akhtari, A. Togbé, P. G. Walsh (2009)
Acta Arithmetica
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A. Togbe, P. M. Voutier, P. G. Walsh (2005)
Acta Arithmetica
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Scarowsky, Manny, Boyarsky, Abraham (1986)
International Journal of Mathematics and Mathematical Sciences
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Hideo Yokoi (1974)
Journal für die reine und angewandte Mathematik
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WILHELM LJUNGGREN (1953)
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J.H.E. Cohn (1991)
Mathematica Scandinavica
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Pingzhi Yuan, Jiagui Luo (2010)
Acta Arithmetica
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Yong Zhang (2016)
Colloquium Mathematicae
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Let f ∈ ℚ [X] be a polynomial without multiple roots and with deg(f) ≥ 2. We give conditions for f(X) = AX² + BX + C such that the Diophantine equation f(x)f(y) = f(z)² has infinitely many nontrivial integer solutions and prove that this equation has a rational parametric solution for infinitely many irreducible cubic polynomials. Moreover, we consider f(x)f(y) = f(z)² for quartic polynomials.
Jianhua Chen (2001)
Acta Arithmetica
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Valeriu St. Udrescu (1979)
Journal für die reine und angewandte Mathematik
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Susil Kumar Jena (2014)
Bulletin of the Polish Academy of Sciences. Mathematics
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The Diophantine equation A² + nB⁴ = C³ has infinitely many integral solutions A, B, C for any fixed integer n. The case n = 0 is trivial. By using a new polynomial identity we generate these solutions, and then give conditions when the solutions are pairwise co-prime.
E. Herrmann, I. Járási, A. Pethő (2004)
Acta Arithmetica
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Yang Hai, P. G. Walsh (2010)
Acta Arithmetica
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Ajai Choudhry, Jarosław Wróblewski (2007)
Acta Arithmetica
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