5≡-1 (mod 3)
5^2i≡1 (mod 3)
5^2i+2≡0 (mod 3)
(1)只要滿足n=2i, 即n為偶數(shù), 那么5^n+2必為合數(shù)
3^5≡1 (mod 11), 3^2≡-2 (mod 11)
3^(5k+2)≡-2 (mod 11)
3^(5k+2)+2≡0 (mod 11)
(2)只要滿足n=5k+2, 那么3^n+2必為合數(shù)
只要k為偶數(shù), 那么5k+2必為偶數(shù)
當(dāng)k取所有偶數(shù)(無窮多個)時, n=5k+2可以滿足題意 (也為無窮多個)