Explicație pas cu pas:
a, b, c numere naturale
[tex]\frac{6}{ {a}^{2} + {b}^{2} + {c}^{2} } > 1 \\ {a}^{2} + {b}^{2} + {c}^{2} < 6[/tex]
[tex]{0}^{2} + {0}^{2} + {1}^{2} < 6[/tex]
(a,b,c): (0,0,1), (0,1,0), (1,0,0)
[tex]{0}^{2} + {0}^{2} + {2}^{2} < 6[/tex]
(a,b,c): (0,0,2), (0,2,0), (2,0,0)
[tex]{0}^{2} + {1}^{2} + {1}^{2} < 6[/tex]
(a,b,c): (0,1,1), (1,0,1), (1,1,0)
[tex]{0}^{2} + {1}^{2} + {2}^{2} < 6[/tex]
(a,b,c): (0,1,2), (0,2,1), (1,0,2), (1,2,0), (2,0,1), (2,1,0)
[tex]{1}^{2} + {1}^{2} + {1}^{2} < 6[/tex]
(a,b,c): (1,1,1)
