A Gel'fond type criterion in degree two
Benoit Arbour, Damien Roy (2004)
Acta Arithmetica
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Benoit Arbour, Damien Roy (2004)
Acta Arithmetica
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Acta Arithmetica
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Charles Osgood (1969)
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Sz. Tengely (2003)
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Michael Fuchs (2010)
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Michael Fuchs (2011)
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Goetgheluck, Pierre (1993)
Experimental Mathematics
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Yann Bugeaud, Nicolas Chevallier (2006)
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Stephen Harrap (2012)
Acta Arithmetica
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P. Erdös, P. Szüsz, P. Turán (1958)
Colloquium Mathematicae
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Dong Han Kim, Hitoshi Nakada (2011)
Acta Arithmetica
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Yong Zhang (2016)
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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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