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Search: id:A064083
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| A064083 |
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Zsigmondy numbers for a = 7, b = 1: Zs(n, 7, 1) is the greatest divisor of 7^n - 1^n (A024075) that is relatively prime to 7^m - 1^m for all positive integers m < n. |
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+0
10
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| 6, 1, 19, 25, 2801, 43, 137257, 1201, 39331, 2101, 329554457, 2353, 16148168401, 102943, 4956001, 2882401, 38771752331201, 117307, 1899815864228857, 1129901, 11898664849, 247165843, 4561457890013486057, 5762401, 79797014141614001
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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. A024075, A064078, A064079, A064080, A064081, A064082.
Sequence in context: A157386 A157396 A019430 this_sequence A152249 A167580 A080213
Adjacent sequences: A064080 A064081 A064082 this_sequence A064084 A064085 A064086
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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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