Prove that infinitely many numbers in the sequence {2012, 20122012, 201220122012, 2012201220122012,....} are multiples of 101.

(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