# On perfect powers in products with terms from arithmetic progressions

Acta Arithmetica (1997)

- Volume: 82, Issue: 2, page 147-172
- ISSN: 0065-1036

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topN. Saradha. "On perfect powers in products with terms from arithmetic progressions." Acta Arithmetica 82.2 (1997): 147-172. <http://eudml.org/doc/207086>.

@article{N1997,

author = {N. Saradha},

journal = {Acta Arithmetica},

keywords = {perfect powers; arithmetic progressions; exponential diophantine equations},

language = {eng},

number = {2},

pages = {147-172},

title = {On perfect powers in products with terms from arithmetic progressions},

url = {http://eudml.org/doc/207086},

volume = {82},

year = {1997},

}

TY - JOUR

AU - N. Saradha

TI - On perfect powers in products with terms from arithmetic progressions

JO - Acta Arithmetica

PY - 1997

VL - 82

IS - 2

SP - 147

EP - 172

LA - eng

KW - perfect powers; arithmetic progressions; exponential diophantine equations

UR - http://eudml.org/doc/207086

ER -

## References

top- [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. Zbl0043.04309
- [3] P. Erdős and J. L. Selfridge, The product of consecutive integers is never a power, Illinois J. Math. 19 (1975), 292-301. Zbl0295.10017
- [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. Zbl0122.05001
- [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. Zbl0859.11025
- [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. Zbl0874.11035
- [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. Zbl0709.11004
- [10] T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), 307-344. Zbl0708.11021

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