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We study the problem of estimating the number of points of coincidences of anidealized gap on the set of integers under a given multiplicative function$g:\mathbb{N}\longrightarrow \mathbb{C}$ respectively additive function$f:\mathbb{N}\longrightarrow \mathbb{C}$. We obtain various lower boundsdepending on the length of the period, by varying the worst growth rates of theratios of their consecutive values.

On the pointwise periodicity of multiplicative and additive functions