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There are infinitely many, just like in base 10.

In any base system, the number of perfect squares is the same.

Take the natural (counting) numbers 1, 2, 3, ....

Squaring each of these produces the perfect squares.

As there are an infinite number of natural numbers, there are an infinite number of perfect squares.

The first 10 perfect squares in base 5 are: 15, 45, 145, 315, 1005, 1215, 1445, 2245, 3115, 4005, ...

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Q: What is the number of perfect squares that exist in base 5 system?
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