Question

Exerciutiul 1 repedeee

Answer 1

$\it 300<n<400\ \ \ \ (1)\\ \\ n:7=a\ rest\ 3 \Rightarrow n=7a+3|_{+4} \Rightarrow n+4=7a+7 \Rightarrow n+4\in\ M_7\ \ \ \ (2)\\ \\ n:10=b\ rest\ 6 \Rightarrow n=10b+6|_{+4} \Rightarrow n+4=10b+10 \Rightarrow n+4\in\ M_{10}\ \ \ \ (3)\\ \\ n:14=c\ rest\ 10 \Rightarrow n=14c+10|_{+4} \Rightarrow n+4=14c+14 \Rightarrow n+4\in\ M_{14}\ \ \ \ (4)$

$\it (2),(3),(4) \Rightarrow n+4\in M_7\cap M_{10}\cap M_{14}\\ \\ {[} 7,\ 10,\ 14 ] = 70\\ \\ n+4\in\{70,\ 140,\ 210,\ 280,\ 350,\ 420,\ ...\}|_{-4} \Rightarrow n\in\{66,136,216,276,346,416, ...\}\ \ \ \ (5)\\ \\ (1),\ (5) \Rightarrow n=346$