Răspuns: (x, y) = (0, 0); ( 0, 1,); ( 0, 2 ); ( 0, 3)
( 1, 0); (1, 1); (1, 2); ( 1,3)
( 2,0); (2,1); (2,2); (2,3)
Explicație pas cu pas:
108/(2ˣx3ⁿ) ∈ N
108 are 12 divizori: 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54 si 108
108 = 2²× 3³
x poate fi 0, 1, 2
n = y poate fi: 0, 1, 2, 3
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(x, y) = (0, 0); ( 0, 1,); ( 0, 2 ); ( 0, 3)
=> 108/(2⁰x3⁰) = 108/1 = 108 ∈ N
108/(2⁰x3¹) = 108/3=36
108/(2⁰x3²) = 108/9 = 12
(x, y) = ( 1, 0); (1, 1); (1, 2); ( 1,3)
=> 108/(2¹x3⁰)/108/2 = 54
108/(2¹x3¹)=108/6 = 18
108/(2¹x3²) = 108/18 = 6
108/(2¹x3³) = 108/54 = 2
( x, y) = ( 2,0); (2,1); (2,2); (2,3)
=> 108/(2²x3⁰) = 108/4 = 27 ∈ N
108/(2²x3¹) = 108/12 = 9
108/(2²x3²) = 108/36 = 3
108/(2²x3³) = 108/108 = 1
