# Perfect powers in products of terms in an arithmetical progression III

Acta Arithmetica (1992)

- Volume: 61, Issue: 4, page 391-398
- ISSN: 0065-1036

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topT. N. Shorey, and R. Tijdeman. "Perfect powers in products of terms in an arithmetical progression III." Acta Arithmetica 61.4 (1992): 391-398. <http://eudml.org/doc/206474>.

@article{T1992,

author = {T. N. Shorey, R. Tijdeman},

journal = {Acta Arithmetica},

keywords = {perfect powers in products; exponential diophantine equation; arithmetical progression},

language = {eng},

number = {4},

pages = {391-398},

title = {Perfect powers in products of terms in an arithmetical progression III},

url = {http://eudml.org/doc/206474},

volume = {61},

year = {1992},

}

TY - JOUR

AU - T. N. Shorey

AU - R. Tijdeman

TI - Perfect powers in products of terms in an arithmetical progression III

JO - Acta Arithmetica

PY - 1992

VL - 61

IS - 4

SP - 391

EP - 398

LA - eng

KW - perfect powers in products; exponential diophantine equation; arithmetical progression

UR - http://eudml.org/doc/206474

ER -

## References

top- [1] P. Erdős, Note on the product of consecutive integers (I), J. London Math. Soc. 14 (1939), 194-198. Zbl0021.20704
- [2] P. Erdős, On the product of consecutive integers III, Indag. Math. 17 (1955), 85-90. Zbl0068.03704
- [3] P. Erdős and J. Turk, Products of integers in short intervals, Acta Arith. 44 (1984), 147-174. Zbl0497.10033
- [4] J.-H. Evertse, On the equation axⁿ-byⁿ=c, Compositio Math. 47 (1982), 289-315.
- [5] J.-H. Evertse and J. H. Silverman, Uniform bounds for the number of solutions to Yⁿ=f(X), Math. Proc. Cambridge Philos. Soc. 100 (1986), 237-248. Zbl0611.10009
- [6] T. N. Shorey, On gaps between numbers with a large prime factor II, Acta Arith. 25 (1974), 365-373. Zbl0258.10023
- [7] T. N. Shorey, Perfect powers in values of certain polynomials at integer points, Math. Proc. Cambridge Philos. Soc. 99 (1986), 195-207. Zbl0598.10029
- [8] T. N. Shorey, Perfect powers in products of integers from a block of consecutive integers, Acta Arith. 49 (1987), 71-79. Zbl0582.10012
- [9] T. N. Shorey, Some exponential diophantine equations, in: New Advances in Transcendence Theory, A. Baker (ed.), Cambridge University Press, 1988, 217-229.
- [10] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge Tracts in Math. 87, Cambridge University Press, 1986. Zbl0606.10011
- [11] T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression II, Acta Arith. 53 (1990), 499-504. Zbl0657.10044
- [12] T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), 307-344. Zbl0708.11021
- [13] T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression III, in: Diophantine Approximation and Transcendental Numbers, Luminy 1990, Ph. Philippon (ed.), to appear. Zbl0709.11004

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