▪ Διοφαντικό σύστημα (ΙΙ)

Να βρεθούν οι έξι διαφορετικοί θετικοί ακέραιοι αριθμοί A, B, C και X, Y, Z που ικανοποιούν τις παρακάτω ισότητες:

                                     A+B+C=X+Y+Z

και
                        A^3+B^3+C^3=X^3+Y^3+Z^3
Απάντηση
A = 2, B = 8, C = 10, X = 4, Y = 5, Z = 11
A = 1, B = 10, C = 14, X = 3, Y = 7, Z = 15
A = 1, B = 10, C = 15, X = 4, Y = 6, Z = 16
A = 1, B = 12, C = 15, X = 2, Y = 10, Z = 16
A = 2, B = 10, C = 12, X = 3, Y = 8, Z = 13
A = 3, B = 11, C = 15, X = 5, Y = 8, Z = 16
A = 3, B = 12, C = 18, X = 6, Y = 8, Z = 19
A = 3, B = 15, C = 17, X = 5, Y = 11, Z = 19
A = 4, B = 14, C = 16, X = 7, Y = 9, Z = 18
A = 5, B = 10, C = 11, X = 6, Y = 8, Z = 12
A = 7, B = 14, C = 18, X = 9, Y = 11, Z = 19