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A200146
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Triangle read by rows: T(n, k) = mod(k^(n - 1), n), where 1 <= k < n.
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1
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1, 1, 1, 1, 0, 3, 1, 1, 1, 1, 1, 2, 3, 4, 5, 1, 1, 1, 1, 1, 1, 1, 0, 3, 0, 5, 0, 7, 1, 4, 0, 7, 7, 0, 4, 1, 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 8, 3, 4, 5, 0, 7, 8, 9, 4, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1
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OFFSET
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2,6
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COMMENTS
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Per Fermat's Little theorem, if n is prime, then row n is all 1s. However, if n is composite, that does not necessarily guarantee that the first column 1 is the only one in the row.
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LINKS
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EXAMPLE
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The first seven rows are
1
1, 1
1, 0, 3
1, 1, 1, 1
1, 2, 3, 4, 5
1, 1, 1, 1, 1, 1
1, 0, 3, 0, 5, 0, 7
We observe that the tenth row consists of the numbers 1 to 9 in order. In base 10, the least significant digit of n^9 is the same as that of n.
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MATHEMATICA
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Column[Table[Mod[k^(n - 1), n], {n, 2, 13}, {k, n - 1}], Center] (* Nov 14 2011 *)
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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