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10-adic integer x such that x^7 = -7.
1

%I #13 Aug 08 2019 10:49:03

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

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

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

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

%C This is the 10's complement of A225445.

%H Seiichi Manyama, <a href="/A225448/b225448.txt">Table of n, a(n) for n = 0..10000</a>

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

%e 57^7 == -7 (mod 10^2).

%e 657^7 == -7 (mod 10^3).

%e 7657^7 == -7 (mod 10^4).

%e 87657^7 == -7 (mod 10^5).

%e 987657^7 == -7 (mod 10^6).

%o (PARI) n=0;for(i=1,100,m=(10^i-7);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+O(2^N))^(1/7), 2^N), Mod((-7+O(5^N))^(1/7), 5^N)))), N) \\ _Seiichi Manyama_, Aug 06 2019

%Y Cf. A225445.

%K nonn,base

%O 0,1

%A _Aswini Vaidyanathan_, May 11 2013