Question

Vă rog rezolvarea la punctele B,C, D

Answer 1

$\it b)\ 12\leq n<36|_{+1} \Rightarrow 13\leq n+1<37\ \ \ \ \ (1)\\ \\ (n+1)\ \vdots\ 4\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow n+1\in\{16,\ 20,\ 24,\ 28,\ 32,\ 36\}|_{-1} \Rightarrow\\ \\ \Rightarrow n\in\{15,\ 19,\ 23,\ 27,\ 31,\ 35\}$

c)

$\it 1<n<15|_{\cdot3} \Rightarrow 3<3n<45|_{+2} \Rightarrow 5<3n+2<47\ \ \ \ \ (1)\\ \\ (3n+2)\ \vdots\ 5\ \ \ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 3n+2\in\{10,\ 15,\ 20,\ 25,\ 30,\ 35,\ 40,\ 45\}|_{-2} \Rightarrow \\ \\ \Rightarrow 3n\in\{8,\ 13,\ 18,\ 23,\ 28,\ 33,\ 38,\ 43\} \stackrel{3n\in M_3}{\Longrightarrow}\ 3n\in\{18,\ 33\}|_{:3} \Rightarrow \\ \\ \Rightarrow n\in\{6,\ 11\}$

$\it d)\ 3<n\leq11|_{\cdot5} \Rightarrow 15<5n\leq55|_{+4} \Rightarrow 19<5n+4\leq59 \ \ \ \ \ (1)\\ \\ (5n+4)\ \vdots\ 6\ \ \ \ \ (2)\\ \\ (1),\ (2)\Rightarrow 5n+4\in\{24,\ 30,\ 36,\ 42,\ 48, 54\}|_{-4} \Rightarrow \\ \\ \Rightarrow 5n\in\{20,\ 26,\ 32,\ 38,\ 44,\ 50\} \stackrel{5n\in M_5}{\Longrightarrow}\ 5n\in\{20,\ 50\}|_{:5} \Rightarrow n\in\{4,\ 10\}$