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A322169
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Digits of the 5-adic integer 7^(1/5).
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6
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2, 4, 1, 3, 1, 4, 1, 4, 1, 0, 3, 2, 3, 3, 1, 1, 3, 1, 1, 3, 3, 3, 3, 1, 4, 1, 2, 4, 2, 0, 0, 1, 0, 0, 3, 0, 3, 2, 1, 3, 0, 0, 3, 2, 4, 1, 1, 0, 3, 3, 2, 2, 3, 0, 2, 0, 3, 3, 3, 1, 2, 0, 2, 0, 0, 0, 0, 3, 3, 0, 0, 2, 0, 3, 1, 1, 0, 4, 1, 0, 4, 0, 4, 0, 3, 4, 0, 3
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OFFSET
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0,1
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COMMENTS
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For k not divisible by 5, k is a fifth power in 5-adic field if and only if k == 1, 7, 18, 24 (mod 25). If k is a fifth power in 5-adic field, then k has exactly one fifth root.
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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, 5^5] such that k^5 - 7 is divisible by 5^6 is k = 1047 = (13142)_5, so the first five terms are 2, 4, 1, 3 and 1.
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MAPLE
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op([1, 3], padic:-rootp(x^5-7, 5, 100)); # Robert Israel, Aug 28 2019
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PROG
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(PARI) a(n) = lift(sqrtn(7+O(5^(n+2)), 5))\5^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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