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ronald

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  1. Yes, this can be proven. The proof is relatively simple but it does require knowledge of Euler's theorem and Euler's totient function (See https://en.wikipedia.org/wiki/Euler's_theorem) The proof consists of 3 steps and constructs an explicit palindrome for every number n that is not divisible by 10. This will be a possible solution, but by no means the smallest palindrome divisible by n. In fact the constructed palindrome get very large. 1) Find a solution for n=2k or n=5k for every integer k=1,2,3,.... 2) Find a solution for any value of n that does not contain a factor 2 or 5 3) Find a solution for any value of n that does contain a factor 2 or 5
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