Python 2, 59 55 53 bytes

lambda s:s in[len(s)/i*s[:i]for i in range(1,len(s))]

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Recursive version:

Python 2, 59 54 bytes

f=lambda s,i=1:s[i+1:]and f(s,i+1)or s==len(s)/i*s[:i]

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Boring regex version:

Python 2, 44 bytes

lambda s:re.match(r'(.+)\1+$',s)>0
import re

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