i was having trouble coming up with an induction proof for this problem, although i have tried and was able to prove it sumhow(using numbers 1 n so forth, teacher doesn't allow us to use them yet), but not using induction. I have no clue on how to do this using induction. plz help me. Problem: Prove that for all n>=12, there are non-negative integers a and b such that n=7a+3b. THen note that if a,b are integers such that 7a+3b>=12, then a>=2 and b>=2. Then put the above property so that having the expression n of the type (n=7a+3b) gives an expression for n+1 also for the type (n=7a+3b). how am i suppose to start this proof, using induction and using facts if needed.