Find the smallest number that can be expressed as the sum of two (nonzero) perfect squares in *two different ways*.

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And what if the two perfect squares must be nonzero, positive, and different?

(In reply to

A hardy perennial by Penny)

Penny writes:

*"...1729 is the smallest number that can be expressed as the sum of two perfect squares in two different ways."*

This is incorrect (for BOTH questions).

I would encourage people to VERIFY their solutions before citing some example from the internet.