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kth power residue chains of global fields

2011
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Glasnik Matematicki - Serija III
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In 1974, Vegh proved that if k is a prime and m a positive integer, there is an m term permutation chain of kth power residue for infinitely many primes (E.Vegh, kth power residue chains, J. Number Theory 9 (1977), 179-181). In fact, his proof showed that 1, 2, 2 2 , . . . , 2 m−1 is an m term permutation chain of kth power residue for infinitely many primes. In this paper, we prove that for any "possible" m term sequence r 1 , r 2 , ..., rm, there are infinitely many primes p making it an m

doi:10.3336/gm.46.1.03
fatcat:wn4kngcidbds7j5srkt5cw4zdy