A225442 - OEIS

%I #12 Aug 16 2019 14:03:15

%S 7,3,4,7,5,2,2,0,4,1,9,0,8,3,4,1,0,5,3,3,0,9,6,5,3,4,9,0,4,7,7,0,5,1,

%T 3,8,2,2,9,9,9,1,8,0,6,9,5,8,3,9,8,1,4,6,7,1,1,3,0,5,0,5,2,2,8,8,5,7,

%U 7,9,5,1,5,8,3,6,5,0,4,7,7,9,0,1,3,7,7,9,2,8,9,8,4,4,2,7,6,5,4,3

%N 10-adic integer x such that x^7 = -1/3.

%H Seiichi Manyama, <a href="/A225442/b225442.txt">Table of n, a(n) for n = 0..10000</a>

%e        7^7 == 3      (mod 10).

%e       37^7 == 33     (mod 10^2).

%e      437^7 == 333    (mod 10^3).

%e     7437^7 == 3333   (mod 10^4).

%e    57437^7 == 33333  (mod 10^5).

%e   257437^7 == 333333 (mod 10^6).

%o (PARI) n=0;for(i=1,100,m=(10^i-1)/3;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((-1/3+O(2^N))^(1/7), 2^N), Mod((-1/3+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