49^m – 33^n
I can’t stand the lack of activity, so here’s a semi-rubbish problem.
1. If x = 49^m – 33^n, where m and n are positive integers, what is the smallest (in magnitude) positive and negative value of x, and what are the corresponding values of m and n? Prove your answer.
2. The above is easy. The next might be very difficult or impossible to do. Are there any other values of m and n that produce the minimal x’s?
3. What’s the second smallest values of x and the associated m and n?
4. Again might be difficult/impossible, are there other values for m and n in part 3?