Abstract
This paper examines the question of whether a given pattern x,x+a 1,…,x+a m−1 of kth power residues of length m can be postponed indefinitely. This is the case when there exists a prime q, called a delay prime, which does not contain this pattern even if q itself is considered as a kth power residue. It is conjectured that if there exists no delay prime then there exists a finite limit Λ=Λ (k,m;a 1,…,a m−1 for which the corresponding pattern will occur before Λ in every sufficiently large prime of the form kn + 1.
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