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Mar 6, 2020 at 11:02 comment added Wojowu @SylvainJULIEN Thanks, the typo was a missing factor. I don't know to what extent the result holds if $q$ has small factors. I suspect that if it has few factors below $\log q$ (something like, their product is $(\log q)^{O(1)}$), then the result remains valid.
Mar 6, 2020 at 11:01 history edited Wojowu CC BY-SA 4.0
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Mar 6, 2020 at 10:59 comment added Sylvain JULIEN Also, the hypothesis is "a number $q$ with no prime factors below $\log q$" but does the theorem apply if some prime factors of $q$ are below $\log q$ while others are bigger?
Mar 6, 2020 at 10:45 comment added Sylvain JULIEN Your answer is instructive but there must be a typo cause the interval to which $x$ belongs is empty.
Mar 6, 2020 at 9:53 vote accept Sylvain JULIEN
Mar 6, 2020 at 9:50 history answered Wojowu CC BY-SA 4.0