Răspuns:
Explicație pas cu pas:
a) NU
[tex]24=2^{3}\cdot3\\72=2^{3}\cdot3^{2} \\(24;72)=2^{3}\cdot3=24[/tex]
b)
a + b = 96 ; (a,b) = 12
[tex]a = 12 \cdot m\\b = 12 \cdot n\\(m,n) = 1[/tex]
[tex]12m+12n=96\\12(m+n)=96\\m+n=8[/tex]
m si n sunt prime intre ele:
[tex]m = 1 \implies n = 7 \implies a = 12;\ b = 84\\m = 3 \implies n = 5 \implies a = 36;\ b = 60\\m = 5 \implies n = 3 \implies a = 60;\ b = 36\\m = 7 \implies n = 1 \implies a = 84;\ b = 12\\[/tex]
[tex](a,b) \in \{(12;84),(36;60),(60;36),(84;12)\}[/tex]
