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Goresky and Klapper conjectured that for any prime p > 13 and any-sequence a based on p, every pair of allowable decimations of a is cyclically distinct. The conjecture is essentially equivalent to the statement that the mapping x → Ax d , with (d, p − 1) = 1, p A, is a permutation of the even residues (mod p) if and only if d = 1 and A ≡ 1 (mod p) for p > 13. We prove the conjecture for p > 2.26 • 10 55 and establish it in a number of other special cases such as when −.000274p < d < .000823p.

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