One day at noon, three teachers bought boxed lunches. If you buy 4 boxes and eat them separately, everyone will be full and there will still be leftovers. At this time, another teacher came, but it turned out that buying another box was not enough for everyone to eat. Later, a few more teachers came, and after buying a few more boxes of lunch, it was just enough for everyone to eat. If every teacher has the same amount of food, how many teachers came at least later?
某天中午，3个老师买盒饭吃．如果买4盒分着吃可以让大家都吃饱，而且还有剩余．此时又来了一位老师，结果发现再多买一盒还不够大家吃．后来又来了若干位老师，结果再多买几盒盒饭后，不多不少刚好够大家吃．如果每个老师的饭量都一样，那么后来至少再来了多少位老师？
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