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Search: id:A064081
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| A064081 |
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Zsigmondy numbers for a = 5, b = 1: Zs(n, 5, 1) is the greatest divisor of 5^n - 1^n (A024049) that is relatively prime to 5^m - 1^m for all positive integers m < n. |
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+0
8
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| 4, 3, 31, 13, 781, 7, 19531, 313, 15751, 521, 12207031, 601, 305175781, 13021, 315121, 195313, 190734863281, 5167, 4768371582031, 375601, 196890121, 8138021, 2980232238769531, 390001, 95397958987501, 203450521
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OFFSET
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1,1
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COMMENT
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By Zsigmondy's theorem, the n-th Zsigmondy number for bases a and b is not 1 except in the three cases (1) a = 2, b = 1, n = 1, (2) a = 2, b = 1, n = 6, (3) n = 2 and a+b is a power of 2.
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REFERENCES
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K. Zsigmondy, Zur Theorie der Potenzreste, Monatshefte fuer Mathematik und Physik 3 (1882), 265 - 284
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LINKS
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K. Zsigmondy, Zur Theorie der Potenzreste, Monatsh. f. Math. III. 265-284. Published 1892.
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CROSSREFS
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Cf. A024049, A064078, A064079, A064080, A064082, A064083.
Sequence in context: A035048 A072044 A127138 this_sequence A099438 A002178 A013558
Adjacent sequences: A064078 A064079 A064080 this_sequence A064082 A064083 A064084
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KEYWORD
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nonn,new
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AUTHOR
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Jens Voss (jens.voss(AT)poet.de), Sep 04 2001
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)eunet.rs), Sep 06 2001
Definition corrected by Jerry Metzger, Nov 04 2009
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