Find all functions which satisfy the following conditions is strictly increasing; for all for all .
Originally Posted by Sorombo
I found one, but only by trial and errors.
If you assume the function is linear then it's easy. Let f(n) = ax + b and you'll get two equations in a and b. They're pretty easy to solve. The only possible result is 2n + 3. Now, why can't we do this with a quadratic?