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A124224
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Table T(n,k) = reciprocal of k-th number prime to n, modulo n, for 1 <= k <= phi(n).
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2
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0, 1, 1, 2, 1, 3, 1, 3, 2, 4, 1, 5, 1, 4, 5, 2, 3, 6, 1, 3, 5, 7, 1, 5, 7, 2, 4, 8, 1, 7, 3, 9, 1, 6, 4, 3, 9, 2, 8, 7, 5, 10, 1, 5, 7, 11, 1, 7, 9, 10, 8, 11, 2, 5, 3, 4, 6, 12, 1, 5, 3, 11, 9, 13, 1, 8, 4, 13, 2, 11, 7, 14, 1, 11, 13, 7, 9, 3, 5, 15, 1, 9, 6, 13, 7, 3, 5, 15, 2, 12, 14, 10, 4, 11, 8, 16
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OFFSET
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1,4
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COMMENTS
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T(n,k) = smallest m such that A038566(n,k) * m = 1 (mod n).
For n>1 every row begins with 1 and ends with n-1. T(n,k) = A038566(n,k)^(phi(n) - 1) (mod n). - Geoffrey Critzer, Jan 03 2015
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LINKS
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FORMULA
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EXAMPLE
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The table T(n,k) starts:
n\k 1 2 2 3 4 5 6 7 8 9 10 11
1: 0
2: 1
3: 1 2
4: 1 3
5: 1 3 2 4
6: 1 5
7: 1 4 5 2 3 6
8: 1 3 5 7
9: 1 5 7 2 4 8
10: 1 7 3 9
11: 1 6 4 3 9 2 8 7 5 10
12: 1 5 7 11
13: 1 7 9 10 8 11 2 5 3 4 6 12
14: 1 5 3 11 9 13
15: 1 8 4 13 2 11 7 14
16: 1 11 13 7 9 3 5 15
...
n = 17: 1 9 6 13 7 3 5 15 2 12 14 10 4 11 8 16,
n = 18: 1 11 13 5 7 17,
n = 19: 1 10 13 5 4 16 11 12 17 2 7 8 3 15 14 6 9 18,
n = 20: 1 7 3 9 11 17 13 19.
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MAPLE
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0, seq(seq(i^(-1) mod m, i = select(t->igcd(t, m)=1, [$1..m-1])), m=1..100); # Robert Israel, May 18 2014
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MATHEMATICA
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Table[nn = n; a = Select[Range[nn], CoprimeQ[#, nn] &];
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CROSSREFS
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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