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A206825 Number of solutions (n,k) of k^4=n^4 (mod n), where 1<=k

%I A206825 #8 Nov 17 2017 20:31:54
%S A206825 0,0,1,0,0,0,3,2,0,0,1,0,0,0,7,0,2,0,1,0,0,0,3,4,0,8,1,0,0,0,7,0,0,0,
%T A206825 5,0,0,0,3,0,0,0,1,2,0,0,7,6,4,0,1,0,8,0,3,0,0,0,1,0,0,2,15,0,0,0,1,0,
%U A206825 0,0,11,0,0,4,1,0,0,0,7,26,0,0,1,0,0,0,3,0,2,0,1,0,0,0,7,0,6,2
%N A206825 Number of solutions (n,k) of k^4=n^4 (mod n), where 1<=k<n.
%H A206825 Antti Karttunen, <a href="/A206825/b206825.txt">Table of n, a(n) for n = 2..16384</a>
%e A206825 8 divides exactly three of the numbers 8^4-k^4 for k = 1, 2 , ..., 7, so that a(8) = 3.
%t A206825 s[k_] := k^4;
%t A206825 f[n_, k_] := If[Mod[s[n] - s[k], n] == 0, 1, 0];
%t A206825 t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]
%t A206825 a[n_] := Count[Flatten[t[n]], 1]
%t A206825 Table[a[n], {n, 2, 120}]  (* A206825 *)
%o A206825 (PARI) A206825(n) = { my(n4 = n^4); sum(k=1,n-1,!((n4-(k^4))%n)); }; \\ _Antti Karttunen_, Nov 17 2017
%Y A206825 Cf. A206590.
%K A206825 nonn
%O A206825 2,7
%A A206825 _Clark Kimberling_, Feb 12 2012