1. The problem statement, all variables and given/known data Find the least positive integer N such that every integer [tex]n \geq N[/tex] can be written in the form 4a + 7b, where a,b are non-negative integers. Prove your N has this property 2. Relevant equations 3. The attempt at a solution Well, I kind of went about doing trial and error. I know 17 is not such a number, but 18,19,20,21,22 are. I figured I'd use (strong) induction. Suppose it's true for all [tex]22 \leq k \leq n[/tex]. Consider now [tex] 18 \leq n+1 -4 < n [/tex]. By the induction hypothesis n+1 -4 = 4a + 7b, so n+1 = 4(a+1) +7b, for some non-negative a,b. Is this correct? What if I wanted to do it more generally. That is, if gcd(x,y)=1 find N such that, for all [tex]n \geq N[/tex], n can be written as xa+yb, for non-negative a,b?