Ken has made a selection of square jam sandwiches for a party, which he arranges in a single layer on the table in a perfect rectangle. Sarah has bought along the same number of square peanut butter sandwiches, which she puts out, also as a single layer, to form a border (one sandwich wide) around ken's rectangle. Given that all of the sandwiches are the same size and they are all used, how many sandwiches could each person possibly have made?
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