\[\begin{array}{l} c)\,\,\forall n \in N,\,\,3{n^2} + 15n + 12\,\,\, \vdots \,\,6\\ A = 3{n^2} + 15n + 12 = 3\left( {{n^2} + 5n + 4} \right)\\ = 3\left( {n + 1} \right)\left( {n + 4} \right)\\ Ta\,\,co:\,\,\,A\,\, \vdots \,\,3\,\,\forall n\\ De\,\,CM\,\,\,A\,\, \vdots \,\,6\,\,\,ta\,\,\,can\,\,\,CM\,\,\,A\,\, \vdots \,\,2\\ Ta\,\,co:\,\,\,\left( {n + 1} \right)\,\,\,va\,\,\left( {n + 4} \right)\,\,\,la\,\,\,1\,\,\,so\,\,le\,\,\,va\,\,\,1\,\,\,so\,\,chan\,\,\,voi\,\,\,\forall n\\ \Rightarrow \left( {n + 1} \right)\left( {n + 4} \right)\,\,\,la\,\,\,1\,\,\,so\,\,chan.\\ \Rightarrow \left( {n + 1} \right)\left( {n + 4} \right)\,\, \vdots \,\,2\,\,\,\forall n\\ \Rightarrow A = 3\left( {n + 1} \right)\left( {n + 4} \right)\,\,\, \vdots \,\,\,6\,\,\,\forall n.\\ b)\,\,\,\forall n \in N:\,\,{n^3} + n + 1\,\,\, \vdots \,\,\,3\\ Cau\,\,nay\,\,\,e\,\,gui\,\,\,de\,\,day\,\,du\,\,nhe, \end{array}\]

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