On perfect powers in products with terms from arithmetic progressions

• Autorzy: N. Saradha
• Języki publikacji: EN

Kategorie tematyczne

• 11D61: Exponential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 2
• Strony: 147-172

Daty

wydano

1997

otrzymano

1996-10-25

poprawiono

1997-03-14

Twórcy

autor

N. Saradha

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

Bibliografia

• [1] L. E. Dickson, History of the Theory of Numbers, Vol. II, Chelsea, New York, 1952.
• [2] P. Erdős, On a Diophantine equation, J. London Math. Soc. 26 (1951), 176-178.
• [3] P. Erdős and J. L. Selfridge, The product of consecutive integers is never a power, Illinois J. Math. 19 (1975), 292-301.
• [4] D. H. Lehmer, List of prime numbers from 1 to 10006721, Carnegie Institution of Washington, Publication No. 165, 1914.
• [5] D. S. Mitrinović, J. Sandor and B. Cristici, Handbook of Number Theory, Kluwer, 1996.
• [6] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94.
• [7] T. N. Shorey and Yu. V. Nesterenko, Perfect powers in products of integers from a block of consecutive integers (II), Acta Arith. 76 (1996), 191-198.
• [8] T. N. Shorey and R. Tijdeman, Some methods of Erdős applied to finite arithmetic progressions, in: The Mathematics of Paul Erdős I, R. L. Graham and J. Nešetřil (eds.), Springer, 1997, 251-267.
• [9] T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression, in: A Tribute to Paul Erdős, A. Baker, B. Bollobás and A. Hajnal (eds.), Cambridge University Press, 1990, 385-389.
• [10] T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), 307-344.