How many integers between 200 and 300 are perfect squares?
You can also use a progression.
Say , (note difference ).
How many terms between and ?
Start from the biggest square under , which is . Now many with can you fit in ?
Is there any sum of terms of with and starting from consecutive that fit into ? Sure ! We have , but we cannot fit , so there are only three perfect squares between and .
There ... must be a better way to explain this, though ..
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I know this solution is a bit useless and boring after the previous answers, but eh, this is worth a post