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Well, there is 16, 64, 144,

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In this problem, the squared number must be a whole number and divisible by 4. 20^2 is 400. And there are 4, 8, 12, 16 ,20; 5 number divisible by 4. and 23^2 is already 529. the next number divisible by 4 is 24 which is over 500. So there are 5 numbers. They are 16, 64, 144, 256, 400.

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