Question: In Example 2.52 why didn't we include the odd integers between 2 and 26? Suppose that we start with the universe that comprises only the

In Example 2.52 why didn't we include the odd integers between 2 and 26?
Suppose that we start with the universe that comprises only the 13 integers 2, 4, 6, 8,..., 24, 26. Then we can establish the statement:
For all n (meaning n = 2, 4, 6, ... , 26),
we can write n as the sum of at most three perfect squares.
The results in Table 2.24 provide a case-by-case verification showing the given (quantified) statement to be true. (We might call this statement a theorem.)

2 1+1 10 9+1 12 44 +4 14 9+4+1 16 16 18 1611 2016+ 4 22 99+4 24 16+4+4 26 25 1 6 41+1 8 4+4

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