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# 3-2-ary numbers

Prove that every positive integer can be expressed as a sum of numbers of the kind $2^i3^j$, where no term in the summation divides the other.

For example :

1) 14 = 8 + 6 is a valid representation, while 14 = 2 + 4 + 8 is invalid since 2|4 and 2|8.

2) 20 = 12 + 8 is fine, but 20 = 18 + 2 is not valid.

Can you find this representation algorithmically.

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Posted: Jun 06 '12

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Last updated: Jun 06 '12