A note on perfect powers of the form xm-1+...+x+1
Maohua Le
Acta Arithmetica, Tome 69 (1995), p. 91-98 / Harvested from The Polish Digital Mathematics Library
Publié le : 1995-01-01
EUDML-ID : urn:eudml:doc:206674
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     author = {Maohua Le},
     title = {A note on perfect powers of the form $x^{m-1} + ... + x + 1$
            },
     journal = {Acta Arithmetica},
     volume = {69},
     year = {1995},
     pages = {91-98},
     zbl = {0819.11012},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-aav69i1p91bwm}
}
Maohua Le. A note on perfect powers of the form $x^{m-1} + ... + x + 1$
            . Acta Arithmetica, Tome 69 (1995) pp. 91-98. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-aav69i1p91bwm/

[000] [1] M. Aaltonen and K. Inkeri, Catalan’s equation xp-yq=1 and related congruences, Math. Comp. 56 (1991), 359-370.

[001] [2] A. Baker, Rational approximations to ∛2 and other algebraic numbers, Quart. J. Math. Oxford 15 (1964), 375-383. | Zbl 0222.10036

[002] [3] W. F. H. Berwick, Integral Bases, Cambridge Univ. Press, 1927. | Zbl 53.0142.01

[003] [4] J. W. S. Cassels, On the equation ax-by=1, II, Math. Proc. Cambridge Philos. Soc. 56 (1960), 97-103. | Zbl 0094.25702

[004] [5] L.-K. Hua, Introduction to Number Theory, Springer, Berlin, 1982.

[005] [6] S. Lang, Algebraic Number Theory, Addison-Wesley, Reading, Massachusetts, 1970. | Zbl 0211.38404

[006] [7] M.-H. Le, A note on the equation (xm-1)/(x-1)=yn+1, Math. Proc. Cambridge Philos. Soc. 115 (1994), to appear.

[007] [8] W. Ljunggren, Noen setninger om ubestemte likninger av formen (xn-1)/(x-1)=yq, Norsk Mat. Tidsskr. 25 (1943), 17-20.

[008] [9] W. Ljunggren, On an improvement of a theorem of T. Nagell concerning the diophantine equation Ax³ + By³ = C, Math. Scand. 1 (1953), 297-309. | Zbl 0051.27803

[009] [10] T. N. Shorey, Perfect powers in values of certain polynomials at integer points, Math. Proc. Cambridge Philos. Soc. 99 (1986), 195-207. | Zbl 0598.10029

[010] [11] T. N. Shorey, On the equation zq=(xn-1)/(x-1), Indag. Math. 48 (1986), 345-351. | Zbl 0603.10018

[011] [12] C. L. Siegel, Die Gleichung axn-byn=c, Math. Ann. 144 (1937), 57-68.