Are the two statements concening number theory correct? Statement 1: any integer no less than four can be factorized as a linear combination of two and three.
Statement 2: any integer no less than six can be factorized as a linear combination of three, four and five.
I tried for many numbers, it seems the above two statement are correct. For example, 
4=2+2; 5=2+3; 6=3+3+3; ...
6=3+3; 7=3+4; 8=4+4; 9=3+3+3; 10=5+5; ...
Can they be proved?

Hints:


*

*Use the division algorithm: $n=2q+r.$ What are the values of $r$? If $n≥4,$ then $q≥2,$ and we can re-write $n$ as: $$n=2(q−1)+2+r.$$ What are the values of $2+r$?

*Again use the division algorithm: $n = 3q + r,$ and with $n ≥ 6,$ we have $$n = 3(q-1) + 3 + r.$$ What are the possible values for $3 + r$?
