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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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123498765 | Comment 5 of 8 |
(In reply to Generalizing a lot by Steve Herman)

No number in the sequence 2012, 20122012, 201220122012... is divisible by 123498765. The number 123498765 is divisible by 5, so all of its multiples end in 0 or 5. However, all of the numbers in this sequence end in 2. Therefore, none of the numbers are divisible by 123498765.



  Posted by Math Man on 2012-05-01 09:29:17
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