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

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, 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, 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

Offset: 2

Author

Clark Kimberling, Feb 12 2012

Keywords

• nonn

Examples

			8 divides exactly three of the numbers 8^4-k^4 for k = 1, 2 , ..., 7, so that a(8) = 3.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 2..16384

Crossrefs

Cf. A206590.

Programs

Mathematica

s[k_] := k^4;
f[n_, k_] := If[Mod[s[n] - s[k], n] == 0, 1, 0];
t[n_] := Flatten[Table[f[n, k], {k, 1, n - 1}]]
a[n_] := Count[Flatten[t[n]], 1]
Table[a[n], {n, 2, 120}]  (* A206825 *)

PARI

A206825(n) = { my(n4 = n^4); sum(k=1,n-1,!((n4-(k^4))%n)); }; \\ Antti Karttunen, Nov 17 2017