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No, not necessarily. 121 is a palindrome number with 3 digits (odd) and is divisible by 11. So this satisfies the premise, but 101, 111, 131, etc are not divisible by 11.

An example which satisfies the premise does not prove it true, but one which contradicts the premise is enough to prove it false.

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Q: Odd number of digits in a palindrome to be divisible by 11?
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