Originally Posted by

**Taluivren** to make it a little more interesting lets suppose k and m must be positive integers.

We have two suitable ways how to add 1:

a) **-3***3 **+2***5

b) **+2***3 **-1***5

we're starting with

16 = **2***3+**2***5. So we are forced to use b) to keep coefficients positive:

17 = **4***3+**1***5 now we are forced to use a) to keep coefficients positive:

18 = **1***3+**3***5 now we are forced to use b) to keep coefficients positive:

19 = **3***3+**2***5 now we must use b):

20 = **5***3+**1***5 and now we must use a):

21 = **2***3+**3***5.

And now we see we're safe: after this five steps we raised coefficients 2,2 to 2,3 and we avoided to sink to 0 (for each coefficient) along the way. So continuing with repeating the seqence babba again and again will get us to every integer >16 without sinking any of the coefficients to 0 along the way.