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 s

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?