Question

Aflati a,b,c numere prime astfel încât a+2b+6c=24

Answer 1

$\displaystyle a+2b+6c=24 \\ \\ a+ \underbrace{2(b+3c)}_{\mbox{par}}=24,~si~cum~24~este~par,~rezulta~ca~a~este~par. \\ \\ a=prim~si~par \Rightarrow a=2. \\ \\ 2+2b+6c=24 \\ \\ 2b+6c=22 \\ \\ b+3c=11. \\ \\ Rezulta~3c\ \textless \ 11,~deci~c \in \{2,3 \}. \\ \\ Daca~c=2 \Rightarrow b=11-3c=11-6=5. \\ \\ Daca~c=3 \Rightarrow b=11-3c=11-9=2. \\ \\ Solutie:~(a,b,c) \in \{(2,5,2);(2,2,3) \}.$

Answer 2

a+2b+6c=24
8+2×2+6×2=24
8+4+12=24
a=8
b=4
c=12