OG11 DS 101題

[mignon]

這是OG11 DS 101題:

If S is the infinite sequence S1=9,S2=99,S3=999,...,Sk=(10的k次方)-1,..., is every term in S divisible by the prime number p?
(1) p is greater than 2.
(2) At least one term in sequence S is divisible by p.

不太瞭解題目要的是什麼,有人可以解釋嗎?尤其是(2),
謝謝!

[mauricew]

數列9, 99, 999, 9999, 99999,..................
是否每一項可以被p整除？
(1)
prime number greater than 2: 3, 5, 7, 11......

S1=9,S2=99,S3=999,...,Sk=(10的k次方)-1,...,

Sk的每一項一定可以被3 整除
但每一項並不一定能被5,7,11,13,17...整除..............insufficient

(2)至少有項Sk,可以被p整除
以S2=99來說, p可以是3, 9, 11
但S1=9時, p卻不可能11,因為無法整除9..............insufficient

(1)+(2)
（1)p是大於2的質數 與 (2)可以整除任何一項的p
兩個交集有太多解了......................................insufficient