Given a polynomial equation in *3* (for any value of
*3*) variables, which is at most quadratic in any variable,
what does the solution space look like? See more
information.

In a finite field of order p^k, the solutions to Markoff:

p = 2, k = 2, number solutions = 17, number components = 3 p = 2, k = 3, number solutions = 65, number components = 4 p = 2, k = 4, number solutions = 257, number components = 5 p = 3, k = 2, number solutions = 81, number components = 17 p = 3, k = 3, number solutions = 729, number components = 92 p = 3, k = 4, number solutions = 6561, number components = 881 p = 5, k = 2, number solutions = 701, number components = 8 p = 5, k = 3, number solutions = 16001, number components = 7

For k=1, these solutions seem to be connected (except for (0,0,0) solution, which is always a singleton). For k>1, this is not true. How many connected components?