write a palindrome number of 6 digits and verify whether it is divisible by 11 or not
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11: that's obviously divisible by 11. ... If this is the case, not only is our six-digit palindrome divisible by 11, but every even digit palindrome is, since we will be able to convert, as above, all even digit palindromes into a sum of terms, such that each term is a multiple of a number of the form 100
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