Divisible Palindromes

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Let n be the number of palindromes consisting only of 1s and 0s that have exactly 2014 digits and are divisible by 11. n can be expressed in the form \( a^b \) where \( a,b \in \mathbb{N} \) and \( a \) is as small as possible but \( a \ne 1 \). Find \( \dfrac{b}{a} \). \( \textbf{ Details and Assumptions } \) Despite only consisting of 1s and 0s the palindromes are all in base 10

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