5≡-1 (mod 3)
5^2i≡1 (mod 3)
5^2i+2≡0 (mod 3)
(1)只要满足n=2i, 即n为偶数, 那么5^n+2必为合数
3^5≡1 (mod 11), 3^2≡-2 (mod 11)
3^(5k+2)≡-2 (mod 11)
3^(5k+2)+2≡0 (mod 11)
(2)只要满足n=5k+2, 那么3^n+2必为合数
只要k为偶数, 那么5k+2必为偶数
当k取所有偶数(无穷多个)时, n=5k+2可以满足题意 (也为无穷多个)