How Many Lightbulbs Will Remain Turned On?

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In a scenario with 1,000 light bulbs and 1,000 students, each student toggles the state of specific bulbs based on their student number. The first student turns all bulbs on, while subsequent students toggle bulbs at intervals corresponding to their student number. The key discussion point revolves around determining how many bulbs remain lit after all students have completed their actions. The final conclusion indicates that 50 bulbs will remain turned on. This outcome is derived from the pattern of toggling, which relates to the number of divisors each bulb number has, ultimately leading to the realization that only bulbs corresponding to perfect squares will stay on.
nabliat5
there is a 1000 light bulbs in a room
near each bulb there is a switch which turns the bulb near it on in a push of a button
and turns it off in a second push of a button and turns it on again in the third push of a button.

1000 students come into the room
the first student pushing every button once (thus turning every lighbulb on)
the second student pushes every second button (turned off every even place lightbulb)
the third student pushes every third button
etc..

how many lightbulbs will remain turned on
if all 1000 students will act the same way as before(the 4th will push every 4th button etc..)
 
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uhm...50.
 
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