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%I #12 Aug 16 2019 14:03:10
%S 3,3,6,5,9,8,0,3,1,9,2,2,9,2,4,9,3,1,3,9,4,0,7,4,3,6,7,8,6,4,6,8,1,7,
%T 7,1,3,8,8,0,1,7,8,4,6,0,3,0,1,0,0,2,8,0,2,4,3,4,8,2,9,2,3,5,5,4,1,3,
%U 5,3,1,0,7,0,1,1,6,7,9,9,8,1,7,2,0,8,4,1,3,1,7,4,3,5,3,7,0,6,4,2
%N 10-adic integer x such that x^7 = -7/9.
%H Seiichi Manyama, <a href="/A225441/b225441.txt">Table of n, a(n) for n = 0..10000</a>
%e 3^7 == 7 (mod 10).
%e 33^7 == 77 (mod 10^2).
%e 633^7 == 777 (mod 10^3).
%e 5633^7 == 7777 (mod 10^4).
%e 95633^7 == 77777 (mod 10^5).
%e 895633^7 == 777777 (mod 10^6).
%o (PARI) n=0;for(i=1,100,m=7*(10^i-1)/9;for(x=0,9,if(((n+(x*10^(i-1)))^7)%(10^i)==m,n=n+(x*10^(i-1));print1(x", ");break)))
%o (PARI) N=100; Vecrev(digits(lift(chinese(Mod((-7/9+O(2^N))^(1/7), 2^N), Mod((-7/9+O(5^N))^(1/7), 5^N)))), N) \\ _Seiichi Manyama_, Aug 06 2019
%K nonn,base
%O 0,1
%A _Aswini Vaidyanathan_, May 11 2013
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