COMPOSITION OF BINOMIAL POLYNOMIAL

Title & Authors
COMPOSITION OF BINOMIAL POLYNOMIAL
Choi, Eun-Mi;

Abstract
For an irreducible binomial polynomial $f(x) Keywords iterated polynomial;Diophantine equation;ABC conjecture; Language English Cited by References 1. F. Beukers, The Diophantine equation$Ax^P$+$By^q$=$Cz^T$, Duke Math. J. 91 (1998), 61-88 2. N. Bruin, The Diophantine equations$x^2 {\pm} y^4 = {\pm}z^6$and$x^2 + y^8 = z^3$, Compositio Math. 118 (1999), 305-321 3. N. Bruin, On powers as sums of two cubes, in Algorithmic Number theory, Prod. 4th International Symp. Lecture Notes in Computer Science 1838, Springer, New York, (2000), 169-184 4. L. Danielson and B. Fein, On the irreducibility of the iterates of$x^n$- b, Proc. Amer. Math. Soc. 130 (2001), 1589-1597 5. H. Darmon, The equation$x^4-y^4=z^p$, C.R.Math. Rep. Acad. Sci. Canada 15 (1993), 286-290 6. H. Darmon, The equation$x^n+y^n=z^2\;and\;x^n+y^n=z^3$, Int. Math. Res. Notices 10 (1993), 236-274 7. H. Darmon and A. Granville, On the equations$z^m$= F(x, y) and$Ax^p + By^q = Cz^r$; Bull. London Math. Soc. 27 (1995), 513-543 8. H. Darmon and L. Merel, Widning quotients and some variants of Fermat's Last Theorem, J. Reine Angew. Math. 490 (1997), 81-100 9. B. Fein and M. Schacker, Properties of iterates and composites of polynomials, J. London Math. Soc. 54 (1996), 489-497 10. A. Kraus, Sur l'equation$a^3+b^3=c^p$, Experiment Math. 7 (1998), 1-13 11. A. Kraus, On the equation$x^p+y^p=z^r$, A survey, Ramanujan 3 (1999), 315-333 12. R. W. K. Odoni, The Galois theory of iterates and composites of polynomials, Proc. London Math. Soc. 51 (1985), 385-414 13. R. W. K. Odoni, Realising wreath products of cyclic groups as Galois groups, Mathematika 35 (1988), 101-113 14. B. Poonen, Some Diophantine equations of the form$x^n+y^n=z^m\$, Acta Arith. LXXXVI 3 (1998), 193-205

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