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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 ?