Google Software Engineer interview questions

Q.Given an input string S write a function which returns true if it satisfies S = nT. Basically you have to find if a given string can be represented from a substring by iterating it “n” times. n >= 2 An example would suffice – Function should return true if 1) S = “abab” 2) S = “abcdabcd” 3) S = “abcabcabc” 4) S = “zzxzzxzzx” Function should return false if 1) S = “abac” 2) S = “abcdabbd” 3) S = “abcabcefg” 4) S = “zzxzzyzzx” It would be easy to understand if you can give an algo instead of saying use kmp or suffix tree or… I came up with O(n*n) solution. Wondered how to do in O(n)