Find the smallest integer N which satifies:
I did not specify the domains of N, so we could have a discussion and consider several cases
N is a positive integer, and a, b integers.
The least value of N is 1. This occurs for (a, b) = (-2, 1)
Case #2 N, a, b positive integers
It is clear that a and b are integers if and only if both k and 3/(k-l) are integers,
that is. if and only if k = 2 or k = 4.
k = 2 —> (a, b) = (16, 32) —>
k = 4 —> (a, b) = (16, 64) —>
The smallest integer is
Now consider case #3 N positive integer and a, b positive real numbers.