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===Divisibility by any fixed positive integer===
The following property, which is part of the « folklore » (i.e., apparently unpublished as a specific result:<ref> {{citation | last = Pollack | first = P. | title = Two problems on the distribution of
| url = | doi-access = free | arxiv = 2303.14043 }}</ref> see the introduction of this article in which it is stated as having « long been known ») has important consequences. For instance it rules out uniform distribution of the values of <math>\varphi(n)</math> in the arithmetic progressions modulo <math>q</math> for any integer <math>q>1</math>.
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| last = Liu | first = H.-Q.
| journal = Proc. Roy. Soc. Edinburgh Sect. A
| title = On
| volume = 146
| issue = 4
| |||