Perfect powers in products of terms in an arithmetical progression

T. N. Shorey; R. Tijdeman

Compositio Mathematica (1990)

  • Volume: 75, Issue: 3, page 307-344
  • ISSN: 0010-437X

How to cite

top

Shorey, T. N., and Tijdeman, R.. "Perfect powers in products of terms in an arithmetical progression." Compositio Mathematica 75.3 (1990): 307-344. <http://eudml.org/doc/90041>.

@article{Shorey1990,
author = {Shorey, T. N., Tijdeman, R.},
journal = {Compositio Mathematica},
keywords = {exponential diophantine equation; greatest prime factor},
language = {eng},
number = {3},
pages = {307-344},
publisher = {Kluwer Academic Publishers},
title = {Perfect powers in products of terms in an arithmetical progression},
url = {http://eudml.org/doc/90041},
volume = {75},
year = {1990},
}

TY - JOUR
AU - Shorey, T. N.
AU - Tijdeman, R.
TI - Perfect powers in products of terms in an arithmetical progression
JO - Compositio Mathematica
PY - 1990
PB - Kluwer Academic Publishers
VL - 75
IS - 3
SP - 307
EP - 344
LA - eng
KW - exponential diophantine equation; greatest prime factor
UR - http://eudml.org/doc/90041
ER -

References

top
  1. 1 P. Erdös, Note on the product of consecutiue integers (I) and (II), J. London Math. Soc.14 (1939), 194-198 and 245-249. Zbl0026.38801JFM65.1145.01
  2. 2 P. Erdös, On a diophantine equation, J. London Math. Soc.26 (1951), 176-178. Zbl0043.04309MR41156
  3. 3 P. Erdös, On the product of consecutive integers III, Indag. Math.17 (1955), 85-90. Zbl0068.03704MR67915
  4. 4 P. Erdös and J.L. Selfridge, The product of consecutive integers is never a power, Illinois J. Math.19 (1975), 292-301. Zbl0295.10017MR376517
  5. 5 P. Erdös and J. Turk, Products of integers in short intervals, Acta Arith.44 (1984), 147-174. Zbl0497.10033MR774096
  6. 6 J.-H. Evertse, On the equation axn - byn = c, Compositio Math. 47 (1982), 289-315. Zbl0498.10014MR681611
  7. 7 D. Hanson, On a theorem of Sylvester and Schur, Canad. Math. Bull.16 (1973), 195-199. Zbl0271.10003MR340162
  8. 8 H. Iwaniec and J. Pintz, Primes in short intervals, Monatsh. Math.98 (1984), 115-143. Zbl0544.10040MR776350
  9. 9 M. Langevin, Plus grand facteur premier d'entiers en progression arithmétique, Sém. Delange-Pisot-Poitou, 18e année, 1976-77, no. 3, 7 pp. Zbl0373.10006
  10. 10 R. Marszalek, On the product of consecutive elements of an arithmetic progression, Monatsh. Math.100 (1985), 215-222. Zbl0582.10011MR812613
  11. 11 O. Rigge, Uber ein diophantisches Problem, 9th Congress Math. Scand., Helsingfors, 1938, Mercator, Helsingfors, 1939, 155-160. Zbl0021.01003JFM65.0139.02
  12. 12 T.N. Shorey, Perfect powers in values of certain polynomials at integer points, Math. Proc. Camb. Phil. Soc.99 (1986), 195-207. Zbl0598.10029MR817661
  13. 13 T.N. Shorey, Perfect powers in products of integers from a block of consecutive integers, Acta Arith.49 (1987), 71-79. Zbl0582.10012MR913765
  14. 14 T.N. Shorey, Some exponential diophantine equations, New Advances in Transcendence Theory, ed. by A. Baker, Cambridge University Press, 1988, pp. 352-365. Zbl0658.10024MR972011
  15. 15 T.N. Shorey, Some exponential diophantine equations II, Number Theory and Related Topics, Tata Institute of Fundamental Research, Bombay, 1988, pp. 217-229. Zbl0748.11022MR1441334
  16. 16 T.N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression, A Tribute to Paul Erdös, Cambridge Univ. Press, to appear. Zbl0709.11004MR1117031
  17. 17 T.N. Shorey and R. Tijdeman, Perfect powers in arithmetical progression, J. Madras Univ., Section B, 51 (1988), 173-180. Zbl1194.11046
  18. 18 J.J. Sylvester, On arithmetic series, Messenger Math.21 (1892), 1-19 and 87-120. JFM23.0181.02
  19. 19 R. Tijdeman, Applications of the Gel'fond-Baker method to rational number theory, Coll. Math. Jańos Bolyai, 13. Topics in Number Theory (Debrecen, 1974), North-Holland, Amsterdam, 1976, pp. 399-416. Zbl0335.10022MR560494
  20. 20 R. Tijdeman, Diophantine equation and diophantine approximations, Number Theory and Applications, Kluwer Acad. Publ., Dordrecht, 1989, pp. 215-243. Zbl0719.11014
  21. 21 Kunrui Yu, Linear forms in the p-adic logarithms, Acta. Arith.53 (1989), 107-186. Zbl0699.10050MR1027200
  22. 22 Kunrui Yu, Linear forms in p-adic logarithms II, Compositio Math.74 (1990), 15-113. Zbl0723.11034

Citations in EuDML Documents

top
  1. N. Saradha, On perfect powers in products with terms from arithmetic progressions
  2. T. N. Shorey, R. Tijdeman, Perfect powers in arithmetical progression (II)
  3. N. Saradha, Squares in products with terms in an arithmetic progression
  4. T. N. Shorey, R. Tijdeman, Perfect powers in products of terms in an arithmetical progression (II)
  5. R. Balasubramanian, T. N. Shorey, Squares in products from a block of consecutive integers
  6. T. N. Shorey, R. Tijdeman, Perfect powers in products of terms in an arithmetical progression III

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.