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Of course, only an SEO would ever search with 1 result per page, but this shows that something wrong with the results.
If I change to 10 results per page then identical URLs on any one page are filtered out. However, I still find the same URL at the bottom of many pages - at #20, #30, #40, #50 and so on.
I'm not sure if this kind of bug was already reported.
A possible explanation for the behaviour is that there is number of different URLs in Google's database which are merged to the same page (URL). When searching for some phrase Google considers these URLs as different. In a second step, the internal different URLs are replaced by the merged one. In a third step, identical URLs are filtered out from the SERPs. This would explain the behaviour described above. However, this is just a theory. A reason for merging different URLs is identical content, e.g. from mydomain.com and my-domain.com or using 301 redirects.
I still find the same URL at the bottom of many pages - at #20, #30, #40, #50 and so on
I can confirm that this kind of bug does show up - I also have seen the exact same url show up on several pages in the SERP. In the cases I noticed, the bug went away within a week or so. I always felt like this bug could be a window into how Google generates the SERP, but I never had any insight.