SOME Zn−1 TERRACES FROM Zn POWER-SEQUENCES, n BEING AN ODD PRIME POWER
نویسندگان
چکیده
A terrace for Zm is a particular type of sequence formed from the m elements of Zm. For m odd, many procedures are available for constructing power-sequence terraces for Zm; each terrace of this sort may be partitioned into segments, of which one contains merely the zero element of Zm, whereas every other segment is either a sequence of successive powers of an element of Zm or such a sequence multiplied throughout by a constant. We now refine this idea to show that, for m = n − 1, where n is an odd prime power, there are many ways in which power-sequences in Zn can be used to arrange the elements of Zn \ {0} in a sequence of distinct entries i, 1 i m, usually in two or more segments, which becomes a terrace for Zm when interpreted modulo m instead of modulo n. Our constructions provide terraces for Zn−1 for all prime powers n satisfying 0 < n < 300 except for n = 125, 127 and 257.
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