Find all 2 digit base 10 integer pairs (X, Y) such that:
- Y is not larger than X
- (sod(X*Y))^3 equals (sod(X))^2 + (sod(Y))^2
... where sod(n) indicates the sum of digits of n
There are precisely 10 integer pairs in consonance with the provisions governing the puzzle under reference and these are:
X Y
14 73
28 50
46 50
50 64
50 82
73 14
50 28
50 46
64 50
82 50
****** Analytical/ Semi-Analytical Method? I don't know! But I will strive for an independent derivation of such a procedure!!