Let be a monic polynomial which is a power of a polynomial of degree and having simple real roots. For given positive integers with and gcd with whenever , we show that the equation
Soit un polynôme qui est une puissance d’un polynôme de degré et dont les racines réelles sont simples. Etant donnés les entiers positifs satisfaisant pgcd et si , nous démontrons que l’équation
@article{JTNB_1997__9_1_183_0, author = {Saradha, N.}, title = {On blocks of arithmetic progressions with equal products}, journal = {Journal de th\'eorie des nombres de Bordeaux}, pages = {183--199}, publisher = {Universit\'e Bordeaux I}, volume = {9}, number = {1}, year = {1997}, mrnumber = {1469667}, zbl = {0889.11010}, language = {en}, url = {http://www.numdam.org/item/JTNB_1997__9_1_183_0/} }
Saradha, N. On blocks of arithmetic progressions with equal products. Journal de théorie des nombres de Bordeaux, Volume 9 (1997) no. 1, pp. 183-199. http://www.numdam.org/item/JTNB_1997__9_1_183_0/
[1] Bounds for the solutions of the hyperelliptic equation, Proc. Camb. Phil. Soc. 65 (1969), 439-444. | MR | Zbl
,[2] On the irreducibility of certain polynomials, Bull.Amer. Math. Soc. 52 (1946), 844-856. | MR | Zbl
and ,[3] Criteria for the irreducibility of polynomials, Ann. of Math. 34 (1993), 81-94. | JFM | MR | Zbl
and ,[4] On arithmetic progressions with equal products, Acta Arithmetica 68 (1994), 89-100. | MR | Zbl
, and ,[5] On values of a polynomial at arithmetic progressions with equal products, Acta Arithmetica 72 (1995), 67-76. | MR | Zbl
, and ,[6] London Math. Soc. Lecture Note Series, Number Theory, Paris 1992-3, éd. Sinnou David, 215 (1995), 231-244. | MR | Zbl
,