# On the diameter of sets of almost powers

B. M. M. de Weger; C. E. van de Woestijne

Acta Arithmetica (1999)

- Volume: 90, Issue: 4, page 371-385
- ISSN: 0065-1036

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topB. M. M. de Weger, and C. E. van de Woestijne. "On the diameter of sets of almost powers." Acta Arithmetica 90.4 (1999): 371-385. <http://eudml.org/doc/207334>.

@article{B1999,

author = {B. M. M. de Weger, C. E. van de Woestijne},

journal = {Acta Arithmetica},

keywords = {almost powers; upper and lower bounds; size of intervals; simultaneous rational approximation to algebraic numbers},

language = {eng},

number = {4},

pages = {371-385},

title = {On the diameter of sets of almost powers},

url = {http://eudml.org/doc/207334},

volume = {90},

year = {1999},

}

TY - JOUR

AU - B. M. M. de Weger

AU - C. E. van de Woestijne

TI - On the diameter of sets of almost powers

JO - Acta Arithmetica

PY - 1999

VL - 90

IS - 4

SP - 371

EP - 385

LA - eng

KW - almost powers; upper and lower bounds; size of intervals; simultaneous rational approximation to algebraic numbers

UR - http://eudml.org/doc/207334

ER -

## References

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- [2] A. Baker and H. Davenport, The equations 3x² - 2 = y² and 8x² - 7 = z², Quart. J. Math. Oxford Ser. (2) 20 (1969), 129-137.
- [3] M. A. Bennett, Simultaneous rational approximation to binomial functions, Trans. Amer. Math. Soc. 348 (1996), 1717-1738. Zbl0873.11042
- [4] G. V. Chudnovsky, On the method of Thue-Siegel, Ann. of Math. (2) 117 (1983), 325-382. Zbl0518.10038
- [5] W. M. Schmidt, Diophantine Approximation, Lecture Notes in Math. 785, Springer, Berlin, 1980. Zbl0421.10019
- [6] M. M. Sweet, A theorem in Diophantine approximations, J. Number Theory 5 (1973), 245-251. Zbl0267.10044
- [7] J. Turk, Almost powers in short intervals, Arch. Math. (Basel) 43 (1984), 157-166. Zbl0524.10037
- [8] N. Tzanakis and B. M. M. de Weger, On the practical solution of the Thue equation, J. Number Theory 31 (1989), 99-132. Zbl0657.10014
- [9] B. M. M. de Weger, Algorithms for Diophantine Equations, CWI Tract 65, Centrum Wisk. Inform., Amsterdam, 1989, 19-26.
- [10] B. M. M. de Weger and C. E. van de Woestijne, On the power-free parts of consecutive integers, Acta Arith., this issue, 387-395. Zbl0971.11051

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