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2024-04-10 21:07:41
Vì p là SNT và p>3
⇒p có dạng p=3K+1;p=3K+2
Lại có p+2 là SNT nên p=3K+2
Vì p=3K+1 thì p+2=3K+3⋮3 là hợp số(Loại)
Ta có: p+p+2=2p+2=2(p+1)
vì p lẻ nên p+1⋮2
lại có p=3K+2⇒p+1=3k+3⋮3
mà Ư(2;3)=1
⇒p+1⋮6(cùng chia hết cho 2 và 3)
⇒2(p+1)⋮12
Vậy p+p+2⋮12 khi p là SNT lớn hơn 3