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Many Multiples (Posted on 2012-04-30) Difficulty: 2 of 5
Prove that infinitely many numbers in the sequence {2012, 20122012, 201220122012, 2012201220122012,....} are multiples of 101.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (2 votes)

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Egg on my face | Comment 7 of 8 |
Boy, was I wrong.  Wrong about my proof and wrong about the generalization.

Consider the sequence 0, 2, 22, 222, 2222, etc.

It has only one term divisible by 5, not an infinite number.

While the remainders mod 5 do eventually cycle (in this case, with period 1), that does not mean that the first term will be part of that cycle.

And that's where I went wrong. 

  Posted by Steve Herman on 2012-05-01 14:32:42
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