Let 

We need to show that k is not an integer.

Assume, for contradiction, that it is an integer.









For  to have a rational solution,
the discriminant  must be a perfect 
square.

Here , ,  

discriminant = 

In order for this discriminant, , to be a 
perfect square, since it has one factor of 17, the other
factor  must also have a factor of 17.  So there
must be an integer n such that









But the right side is an integer but the left side is not.

This contradicts our assumption that the discriminant is a perfect
square.   

Therefore "a" cannot be a rational number.  And since "a" is
not a rational number, it certainly cannot be an integer.

Edwin