Question

Determina numerele prime a,b, care verifica relatia:3a+2b=16

Answer 1

$3a+2b=16 \\ \\ 3a=16-2b \\ \\ 3a=2(8-b) \\ \\ 3~si~2~sunt~prime~intre~ele \Rightarrow 2 ~|~ a,~dar~a~este~prim \Rightarrow \boxed{a=2}~. \\ \\ 3 \cdot 2+2b=2 \cdot 8~~~~~~~~~~~|:2 \\ \\ 3+b=8 \Rightarrow \boxed{b=5} ~.$