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A091661
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Coefficients in a 10-adic square root of 1.
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13
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9, 4, 2, 1, 8, 7, 5, 2, 4, 6, 3, 8, 9, 1, 5, 2, 1, 5, 4, 8, 7, 4, 5, 9, 9, 3, 2, 3, 1, 2, 8, 0, 0, 8, 1, 2, 2, 9, 7, 1, 6, 4, 6, 4, 8, 6, 4, 8, 4, 1, 1, 1, 0, 0, 2, 2, 6, 7, 2, 7, 1, 6, 1, 9, 1, 0, 3, 3, 3, 4, 2, 1, 0, 8, 7, 9, 1, 0, 7, 7, 8, 5, 0, 6, 9, 3, 3, 6, 1, 2, 8, 3, 6, 4, 1, 0, 6, 0, 9, 7
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OFFSET
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0,1
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COMMENTS
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10-adic integer x=.....239954784512519836425781249 satisfying x^3 = x.
Let a,b be integers defined in A018247, A018248 satisfying a^2=a, b^2=b, obviously a^3=a, b^3=b; let c,d,e,f be integers defined in A091661, A063006, A091663, A091664 then c^3=c, d^3=d, e^3=e, f^3=f, c+d=1, a+e=1, b+f=1, b+c=a, d+f=e, a+f=c, a=f+1, b=e+1, cd=-1, af=-1, gh=-1 where -1=.....999999999.
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LINKS
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FORMULA
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MATHEMATICA
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To calculate c, d, e, f use Mathematica algorithms for a, b and equations: c=a-b, d=1-c, e=b-1, f=a-1.
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PROG
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(Ruby)
def A(s, n)
n.times{|i|
m = 10 ** (i + 1)
(0..9).each{|j|
k = j * m + s
if (k ** 2 - k) % (m * 10) == 0
s = k
break
end
}
}
s
end
str = (10 ** (n + 1) + A(5, n) - A(6, n)).to_s.reverse
(0..n).map{|i| str[i].to_i}
end
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CROSSREFS
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Another 10-adic root of 1 is given by A063006.
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KEYWORD
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base,nonn
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AUTHOR
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Edoardo Gueglio (egueglio(AT)yahoo.it), Jan 28 2004
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STATUS
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approved
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