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Abstract
Euler Perfect Box 2nd Way
a, b, c, d, e, f, g ∈ N_+ ⟺ Euler Perfect Box
Substitute any value of a, b, c into expressions a^2 + b^2+ c^2, & (a + b+ c)^2 in order to know, which one is a complete square!
Example (a+b)^2 = a^2 + 2ab + b^2
(2+3)^2 = 25 & 2^2 +2(2)3 +3^2 = 25, then we know (a+b)^2 & (a^2 + 2ab + b^2) are squares.
But a^2 + ab = 2^2 + 2(3) = 10, then we know a^2 + ab is not a square.