Question

Aflati numerele prime a,b,c stiind ca a+2b+3c =17

Answer 1

$\displaystyle Avem~3c\ \textless \ 17,~deci~c \in \{2,3,5 \}. \\ \\ \bullet Daca~c=5~\Rightarrow a+2b=2,~imposibil! \\ \\ \bullet Daca~c=3 \Rightarrow a+2b=8.~Cum~8~si~2b~sunt~pare,~rezulta~ca \\ \\ a~este~par.~Deci~a=2 \Rightarrow b=3. \\ \\ \bullet Daca~c=2 \Rightarrow a+2b=11.~Deci~2b\ \textless \ 11.~Adica~b \in \{2,3,5 \}. \\ \\ *b=2 \Rightarrow a=7. \\ \\ *b=3 \Rightarrow a=5. \\ \\ *b=5 \Rightarrow a=1,~nu~e~prim!$

$\displaystyle Deci~solutiile~sunt~(a,b,c) \in \{(2,3,3),(7,2,2),(5,3,2) \}.$