A333570 - OEIS

A333570

Number of nonnegative values c such that c^n == -c (mod n).

1, 2, 1, 2, 1, 4, 1, 2, 1, 4, 1, 4, 1, 4, 3, 2, 1, 4, 1, 4, 1, 4, 1, 4, 1, 4, 1, 8, 1, 8, 1, 2, 1, 4, 3, 4, 1, 4, 3, 4, 1, 8, 1, 4, 1, 4, 1, 4, 1, 4, 3, 8, 1, 4, 3, 4, 1, 4, 1, 8, 1, 4, 1, 2, 1, 24, 1, 4, 1, 16, 1, 4, 1, 4, 3, 8, 1, 8, 1, 4, 1, 4, 1, 8, 5, 4, 3, 4, 1, 8, 7, 4, 1, 4, 3

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OFFSET

1,2

COMMENTS

a(n) is the number of nonnegative bases c < n such that c^n + c == 0 (mod n).

a(2^k) = 2 for k > 0.

a(p^m) = 1 for odd prime p with m >= 0.

Let fy(n) = (the number of values b in Z/nZ such that b^y = b)/(the number of values c in Z/nZ such that -c^y = c) for nonnegative y, then:

f0(n) = A000012(n),

f1(n) = A026741(n),

f2(n) = A000012(n),

1 <= f3(n) <= n,