Squares in products with terms in an arithmetic progression

N. Saradha

Acta Arithmetica (1998)

  • Volume: 86, Issue: 1, page 27-43
  • ISSN: 0065-1036

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N. Saradha. "Squares in products with terms in an arithmetic progression." Acta Arithmetica 86.1 (1998): 27-43. <http://eudml.org/doc/207179>.

@article{N1998,
author = {N. Saradha},
journal = {Acta Arithmetica},
keywords = {squares; arithmetic progression; product of consecutive positive integers; diophantine equations},
language = {eng},
number = {1},
pages = {27-43},
title = {Squares in products with terms in an arithmetic progression},
url = {http://eudml.org/doc/207179},
volume = {86},
year = {1998},
}

TY - JOUR
AU - N. Saradha
TI - Squares in products with terms in an arithmetic progression
JO - Acta Arithmetica
PY - 1998
VL - 86
IS - 1
SP - 27
EP - 43
LA - eng
KW - squares; arithmetic progression; product of consecutive positive integers; diophantine equations
UR - http://eudml.org/doc/207179
ER -

References

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  1. [1] T. M. Apostol, Introduction to Analytic Number Theory, Springer, 1976. 
  2. [2] L. E. Dickson, Introduction to the Theory of Numbers, Univ. of Chicago Press, 1946. 
  3. [3] L. E. Dickson, History of the Theory of Numbers, Vol. II, Washington, 1919; reprint: Chelsea, New York, 1971. Zbl47.0100.04
  4. [4] P. Erdős, Note on products of consecutive integers, J. London Math. Soc. 14 (1939), 194-198. Zbl0021.20704
  5. [5] P. Erdős and J. L. Selfridge, The product of consecutive integers is never a power, Illinois J. Math. 19 (1975), 292-301. Zbl0295.10017
  6. [6] W. Ljunggren, New solution of a problem proposed by E. Lucas, Norsk Mat. Tidsskrift 34 (1952), 65-72. Zbl0047.04102
  7. [7] R. Marsza/lek, On the product of consecutive elements of an arithmetic progression, Monatsh. Math. 100 (1985), 215-222. 
  8. [8] A. Meyl, Question 1194, Nouv. Ann. Math. (2) 17 (1878), 464-467. 
  9. [9] L. J. Mordell, Diophantine Equations, Academic Press, 1969. 
  10. [10] I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, Wiley, 1972. Zbl0237.10001
  11. [11] P. Ribenboim, Catalan's Conjecture, Academic Press, 1994. Zbl0824.11010
  12. [12] O. Rigge, Über ein diophantisches Problem, in: 9th Congress Math. Scand., Helsingfors, 1938, Mercator, 155-160. Zbl65.0139.02
  13. [13] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94. Zbl0122.05001
  14. [14] N. Saradha, On perfect powers in products with terms from arithmetic progressions, Acta Arith. 82 (1997), 147-172. Zbl0922.11025
  15. [15] 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 Univ. Press, 1990, 385-389. Zbl0709.11004
  16. [16] T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), 307-344. Zbl0708.11021
  17. [17] G. N. Watson, The problem of the square pyramid, Messenger Math. 48 (1919), 1-22. 

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