A number theory problem by Finn C

Number Theory Level pending

There are 100 people in a room. There are also 100 closed lockers. Each of the 100 people are assigned a number from 1-100. The first person with the number 1, would open every locker since every number from 1-100 is a multiple of one. The second person would close every second locker. The third person would open or close every third locker, for example if locker 52 was open, he would close it. If number 52 was closed he would open it. This process is repeated until every person has opened or closed the lockers they're meant to. Which lockers will be open?

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