I read this as a, b, and N must all be positive integers and we are to find the minimum possible N and which a and b generate that N.
My preliminary exploration was to consider 3a^2>ab^2 for any solution. If 3a=b^2+2 the inequality is satisfied and b^2+2 can be a multiple of 3 when b is coprime to 3.
Then substitute and simplify to get 3N=2*(b-4)*(b+1). Let b=5, then N=4 and a=9. This at least sets a upper bound on the smallest possible integer N.
re: Solution? - and my initial thoughts
