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A225455
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10-adic integer x such that x^9 == (10^n-1)/9 mod 10^n for all n.
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2
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1, 9, 3, 4, 8, 5, 1, 1, 9, 3, 5, 8, 6, 8, 7, 0, 8, 3, 8, 4, 5, 2, 6, 8, 7, 2, 8, 2, 5, 8, 9, 8, 2, 0, 5, 0, 8, 7, 4, 3, 6, 6, 9, 4, 4, 3, 6, 2, 2, 8, 0, 2, 2, 3, 7, 5, 2, 0, 5, 5, 6, 9, 2, 8, 2, 7, 1, 7, 1, 0, 8, 0, 6, 3, 0, 8, 8, 8, 6, 7, 6, 7, 5, 7, 4, 9, 8, 1, 5, 5, 2, 1, 7, 0, 3, 1, 6, 0, 6, 9
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OFFSET
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1,2
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LINKS
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EXAMPLE
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1^9 == 1 (mod 10).
91^9 == 11 (mod 100).
391^9 == 111 (mod 1000).
4391^9 == 1111 (mod 10000).
84391^9 == 11111 (mod 100000).
584391^9 == 111111 (mod 1000000).
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MAPLE
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A[1]:= 1: P:= 1:
for d from 2 to 100 do
R:= (expand((10^(d-1)*x+P)^9 - ((10^d-1)/9)) mod 10^d)/10^(d-1);
A[d]:= subs(msolve(R, 10), x);
P:= subs(10^(d-1)*A[d]+P);
od:
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PROG
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(PARI) n=0; for(i=1, 100, m=(10^i-1)/9; for(x=0, 9, if(((n+(x*10^(i-1)))^9)%(10^i)==m, n=n+(x*10^(i-1)); print1(x", "); break)))
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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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