Squares in products from a block of consecutive integers

• Autorzy: R. Balasubramanian , T. N. Shorey
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1993
• Tom: 65
• Numer: 3
• Strony: 213-220

Daty

wydano

1993

otrzymano

1992-08-17

Twórcy

autor

R. Balasubramanian

• Institute of Mathematical Sciences, Madras 600 113, India

autor

T. N. Shorey

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

Bibliografia

• [1] A. Baker, Bounds for the solutions of the hyperelliptic equation, Proc. Cambridge Philos. Soc. 65 (1969), 439-444.
• [2] P. Erdős, Note on the product of consecutive integers (I), J. London Math. Soc. 14 (1939), 194-198.
• [3] P. Erdős, On the product of consecutive integers III, Indag. Math. 17 (1955), 85-90.
• [4] P. Erdős and J. Turk, Products of integers in short intervals, Acta Arith. 44 (1984), 147-174.
• [5] M. N. Huxley, On the difference between consecutive primes, Invent. Math. 15 (1972), 164-170.
• [6] T. Nagell, Introduction to Number Theory, Wiley, 1951.
• [7] K. Ramachandra, Some problems of analytic number theory, Acta Arith. 31 (1976), 313-324.
• [8] O. Rigge, Über ein diophantisches Problem, in: 9th Congress Math. Scand. Helsingfors, 1938, Mercator, Helsingfors, 1939, 155-160.
• [9] T. N. Shorey, Perfect powers in values of certain polynomials at integer points, Math. Proc. Cambridge Philos. Soc. 99 (1986), 195-207.
• [10] T. N. Shorey, Perfect powers in products of integers from a block of consecutive integers, Acta Arith. 49 (1987), 71-79.
• [11] T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), 307-344.
• [12] V. G. Sprindžuk, Hyperelliptic diophantine equation and class numbers of ideals, Acta Arith. 30 (1976), 95-108 (in Russian).