Exercise
Let x be a nonzero element of Z/pZ, p prime. Consider the pattern D consisting of pairs (i, xi - 1), with 0 < i < p. Which of the following is true?
The pattern D is always optimal.
The pattern is optimal if and only if x is a primitive element.
There are nonprimitive x for which the pattern is optimal.
No, not always!
Yes, if
x is not primitive, say xk = 1 for
some positive k with k < p - 1, then a shift
over (k, 0) will give overlap of (1,1) and (2, x) with
(k + 1, 1) and (k + 2, x).
No, if x is not primitive,
say xk = 1 for
some positive k with k < p - 1, then a shift over (k, 0) will give overlap of (1,1) and (2, x) with (k + 1, 1) and (k + 2, x).