  Lenstra's concept of Euclidean ideals generalizes the Euclidean algorithm; a
domain with a Euclidean ideal has cyclic class group, while a domain with a
Euclidean algorithm has trivial class group. This paper generalizes Harper's
variation of Motzkin's lemma to Lenstra's concept of Euclidean ideals and then
uses the large sieve to obtain growth results. It concludes that if a certain
set of primes is large enough, then the ring of integers of a number field with
cyclic class group has a Euclidean ideal.
