[tex]\it a)\\ \\ x:7=a\ rest\ r \Rightarrow x=7\cdot a+r\\ \\ y:7=b\ rest\ r \Rightarrow y=7\cdot b+r\\ \\ x-y=7\cdot a+r-7\cdot b -r=7\cdot a-7\cdot b =7(a-b) \Rightarrow x-y \in M_7 \Rightarrow \\ \\ \Rightarrow7|(x-y)[/tex]
[tex]\it b)\\ \\ 5|(3x+y)\ \ \ \ (1)\\ \\ 5|5x \Rightarrow 5|(3x+2x)\Rightarrow5|(3x+2x+y-y) \Rightarrow5|[(3x+y) +(2x-y)]\ \ \ (2)\\ \\ (1),\ (2) \Rightarrow 5|(2x-y)[/tex]
