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A324153
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Digits of one of the four 13-adic integers 3^(1/4) that is congruent to 11 mod 13.
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14
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11, 10, 5, 11, 0, 6, 0, 8, 4, 6, 11, 2, 8, 6, 5, 4, 2, 11, 0, 3, 3, 5, 12, 0, 9, 6, 8, 7, 1, 0, 9, 1, 3, 7, 4, 8, 8, 10, 5, 8, 1, 4, 8, 2, 11, 12, 10, 11, 8, 9, 1, 5, 9, 6, 9, 10, 6, 5, 9, 6, 11, 12, 9, 12, 1, 4, 1, 6, 1, 12, 9, 7, 8, 5, 3, 2, 0, 6, 1, 7, 11
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OFFSET
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0,1
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COMMENTS
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One of the two square roots of A322087, where an A-number represents a 13-adic number. The other square root is A324085.
For k not divisible by 13, k is a fourth power in 13-adic field if and only if k == 1, 3, 9 (mod 13). If k is a fourth power in 13-adic field, then k has exactly 4 fourth-power roots.
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LINKS
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FORMULA
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EXAMPLE
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The unique number k in [1, 13^3] and congruent to 11 modulo 13 such that k^4 - 3 is divisible by 13^3 is k = 986 = (5AB)_13, so the first three terms are 11, 10 and 5.
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MAPLE
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R:= select(t -> op([1, 3, 1], t)=11, [padic:-rootp(x^4-3, 13, 101)]):
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PROG
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(PARI) a(n) = lift(-sqrtn(3+O(13^(n+1)), 4) * sqrt(-1+O(13^(n+1))))\13^n
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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