An effective solution of a certain diophantine problem
U. Zannier (1995)
Rendiconti del Seminario Matematico della Università di Padova
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U. Zannier (1995)
Rendiconti del Seminario Matematico della Università di Padova
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Robert Franz Tichy (1994)
Mathematica Slovaca
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Gábor Nyul (2002)
Acta Mathematica et Informatica Universitatis Ostraviensis
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Maurice Mignotte, Attila Petho (1999)
Publicacions Matemàtiques
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We consider the diophantine equation (*) xp - x = yq - y in integers (x, p, y, q). We prove that for given p and q with 2 ≤ p < q, (*) has only finitely many solutions. Assuming the abc-conjecture we can prove that p and q are bounded. In the special case p = 2 and y a prime power we are able to solve (*) completely.
Per Salberger (2005)
Annales scientifiques de l'École Normale Supérieure
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Masao Toyoizumi (1983)
Acta Arithmetica
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Ken Yamamura (2001)
Journal de théorie des nombres de Bordeaux
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In the previous paper [15], we determined the structure of the Galois groups of the maximal unramified extensions of imaginary quadratic number fields of conductors under the Generalized Riemann Hypothesis (GRH) except for 23 fields (these are of conductors ) and give a table of . We update the table (under GRH). For 19 exceptional fields of them, we determine . In particular, for , we obtain , the fourth Hilbert class field of . This is the first example of a number...