abstract
##

Avoiding arithmetic progressions in cyclic groups

Lorenz Halbeisen and Stephanie Halbeisen

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For given natural numbers *n* and *r*, alpha(*n,r*)
denotes the maximum cardinality of a subset of
*Z*_{n}
which does not contain any non-constant arithmetic progression
(modulo *n*) of length *r*. The function
alpha(*n,r*) is investigated for several values of *n* and
*r*. In particular, it is shown that alpha(*n,n*)=*n(1-1/p)
*, where *p* is the smallest prime dividing *n*, and that
for any prime number *p* we have
alpha(*p*^{2},p)=(*p-1*)^{2}.