On the irreducibility of some polynomials in two variables

B. Brindza; Á. Pintér

ArticleOriginal scientific text

Title

On the irreducibility of some polynomials in two variables

Authors , ¹

Affiliations

Mathematical Institute of Kossuth Lajos University, P.O. Box 12, H-4010 Debrecen, Hungary

[BS] R. Balasubramanian and T. N. Shorey, On the equation f(x+1)...f(x+k) = f(y+1)...f(y+mk), Indag. Math. (N.S.) 4 (1993), 257-267.
[DLS] H. Davenport, D. J. Lewis and A. Schinzel, Equations of the form f(x)=g(y), Quart. J. Math. 12 (1961), 304-312.
[MB] R. A. MacLeod and I. Barrodale, On equal products of consecutive integers, Canad. Math. Bull. 13 (1970), 255-259.
[SS] N. Saradha and T. N. Shorey, The equations (x+1)...(x+k) = (y+1)...(y+mk) with m=3,4, Indag. Math. (N.S.) 2 (1991), 489-510.
[SST1] N. Saradha, T. N. Shorey and R. Tijdeman, On the equation x(x+1)...(x+k-1) = y(y+d) ...(y+(mk-1)d), m=1,2, Acta Arith. 71 (1995), 181-196.
[SST2] N. Saradha, T. N. Shorey and R. Tijdeman, On arithmetic progressions with equal products, Acta Arith. 68 (1994), 89-100.
[S1] A. Schinzel, An improvement of Runge's theorem on diophantine equations, Comment. Pontific. Acad. Sci. 2 (1969), no. 20, 1-9.
[S2] A. Schinzel, Reducibility of polynomials of the form f(x)-g(y), Colloq. Math. 18 (1967), 213-218.
[Sh] T. N. Shorey, On a conjecture that a product of k consecutive positive integers is never equal to a product of mk consecutive positive integers except for 8·9·10=6! and related questions, in: Number Theory (Paris, 1992-93), London Math. Soc. Lecture Note Ser. 215, Cambridge Univ. Press, Cambridge, 1995, 231-244.
[ST] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Univ. Press, Cambridge, 1986.
[Y] P. Z. Yuan, On a special Diophantine equation $a {x c h \infty s e n} = b y^{r} + c$ , Publ. Math. Debrecen 44 (1994), 137-143.

Title

On the irreducibility of some polynomials in two variables

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