Question

Tìm x ∈ n biết rằng x+1;x+3;x+7;x+9;x+13;x+15 đều là số nguyên tố.

Answer 1

\(Xét:x=3k\Rightarrow x+3=3k+3⋮3\left(ko\right)x=3k+2\Rightarrow x+1=3k+3⋮3\left(ko\right)\Rightarrow x\div3=n\left(dư1\right)Mặtkhác:x=2k+1\Rightarrow x+1=2k+2⋮2\left(ko\right)\Rightarrow x=2k\left(chẵn\right)\Rightarrow cótc=0;2;4;6;8Xet:x\left(tậncung\right)=2thix+3\left(cótc\right)=5⋮5\left(ko\right)x\left(tc\right)=4\Rightarrow x+1\left(tậncung\right)=5⋮5\left(ko\right)x\left(tậncung\right)=0\Rightarrow x+15\left(tc\right)=5⋮5>5koTuxettiep\Rightarrow x< 10..........\)