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The obvious solution is to make the footnote number reset whenever the page number is stepped, using the LaTeX internal mechanism. Sadly, the place in the document where the page number is stepped is unpredictable, not (“tidily”) at the end of the printed page; so changing the footnote number only ever works by ‘luck’.

As a result, resetting footnotes is inevitably a complicated process, using labels of some sort. It’s nevertheless important, given the common requirement for footnotes marked by symbols (with painfully small symbol sets). There are four packages that manage it, one way or another.

The perpage and zref-perpage packages provide a general mechanism for resetting counters per page, so can obviously be used for this task. The interface is pretty simple: \MakePerPage{footnote} (in perpage) or \zmakeperpage{footnote} (in zref-perpage). If you want to restart the counter at something other than 1 (for example to avoid something in the LaTeX footnote symbol list), you can use: \MakePerPage[2]{footnote} (in perpage) or \zmakeperpage[2]{footnote} (in zref-perpage). Note that you can also load zref-perpage

Perpage is a compact and efficient package; zref-perpage, being a zref “module”, comes with zref’s general mechanism for extending the the \label—\[page]ref of LaTeX, which can offer many other useful facilities.

The footmisc package provides a variety of means of controlling footnote appearance, among them a package option perpage that adjusts the numbering per page; if you’re doing something else odd about footnotes, it means you may only need the one package to achieve your ends.

The footnpag package also does per-page footnotes (and nothing else). With the competition from perpage, it’s probably not particularly useful any more.