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29 = 225 - 196

28 = 64 - 36

27 = 36 - 9

25 = 169 - 144

24 = 25 - 1

23 = 144 - 121

21 = 25 - 4

20 = 36 - 16

19 = 100 - 81

17 = 81 - 64

16 = 25 - 9

15 = 16 - 1

13 = 49 - 36

12 = 16 - 4

11 = 36 - 25

9 = 25 - 16

8 = 9 - 1

7 = 16 - 9

5 = 9 - 4

3 = 4 - 1

1 = 1 - 0 (if you include zero as a square number)

0 = any square number subtracted from itself

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Q: Which numbers under 30 can be made by subtracting two square numbers from each other?
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It is not closed under taking square (or other even) roots.


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With great difficulty. What exactly are you trying to ask?