[tex]a,\;b,\;c~~~sunt~numere ~prime \\
2a+6b+7c=66 \\
2a = numar ~par \\
6b = numar ~par \\
66 = numar~par \\
\Rightarrow~~7c ~trebuie ~sa ~fie~ par. \\
\text{Singurul numar prim par este 2. }
[/tex]
[tex]\Rightarrow~~c=\boxed{2} \\
2a+6b+7\times 2=66 \\
2a+6b=66-14 \\
2a+6b = 52 ~~~~~|:2 \\
a+3b=26 \\
a=26-3b ~~~~~(Dam~valori~lui~b) \\
b=\boxed {1}~~\Longrightarrow~~a=26-3\times 1 = 26-3 = \boxed{23} \\
b=\boxed {3}~~\Longrightarrow~~a=26-3\times 3 = 26-9 = \boxed{17} \\
b=\boxed {5}~~\Longrightarrow~~a=26-3\times 5 = 26-15 = \boxed{11} \\
b=\boxed {7}~~\Longrightarrow~~a=26-3\times 7 = 26-21 = \boxed{5}
[/tex]
[tex]Avem \; solutiile: \\
S1: ~~~\boxed{a=23,~b=1,~c=2} \\
S2: ~~~\boxed{a=17,~b=3,~c=2} \\
S3: ~~~\boxed{a=11,~b=5,~c=2} \\
S4: ~~~\boxed{a=5,~b=7,~c=2} \\
[/tex]
