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Possible Duplicate:
When do the multiples of two primes span all large enough natural numbers?

We have to generate a number by using only 3's and 5's.
For ex :

3 = 3
4 can't be generated
5 = 5
6 = 3 + 3
7 can't be generated
8 = 3 + 5
9 = 3 + 3 + 3
10 = 5 + 5
11 = 3 + 3 + 5
and so on...  

So from 8, every integer i.e. 9,10,11,12,.. can be generated by using 3's and 5's.
But I can't prove it. So

    (i) Is there a way to prove that every integer after 7, can be generated  
        by using only 3's and 5's ?
    (ii)Are there any other pairs of numbers (as 3 and 5 here), which satisfy  
        this property that after certain integer, all integers can be generated  
        by using number only from that pair ?
  • 4
    Yes and yes; see http://math.stackexchange.com/questions/8186/when-do-the-multiples-of-two-primes-span-all-large-enough-natural-numbers/8187#8187.2011-01-07
  • 0
    $7=3+3+3+3-5$ .2011-01-07
  • 1
    $4=3+3+3-5$. (extra characters)2011-01-07
  • 0
    @Jonas Meyer : Thanks for that link.2011-01-07

0 Answers 0