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Extreme Palindrome Exercise (Posted on 2016-04-11) Difficulty: 2 of 5
Determine the respective smallest and largest 3-digit palindromes in base 2017 each of which is divisible by 7.

*** Leading zeros in any of the palindromes is not allowed.

No Solution Yet Submitted by K Sengupta    
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Solution agree Comment 3 of 3 |
ABA in base 2017 is (2017^2 + 1) * A + 2017 * B.

2017 is 1 mod 7; we need the total to be zero mod 0.

For the largest we wand A to be as large as possible: 2016, which is already zero mod 7; we might as well make B 2016 also. The digits are all 2016.

For the smallest, remember that  (2017^2 + 1) is 2 mod 7.  If A is 1, to make ABA small, B must be 5 mod 7, or just plain 5. We have 151. In decimal that's  582625.

  Posted by Charlie on 2016-04-11 10:16:10
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