if a^2-b^2=33 and a^3-b^3=817 have the integer solution with a>b, find the value of a-b
Here's a slightly quicker solution. Since , it follows that is a factor of 33, so it must be or . But is also a factor of . However, 817 is not divisible by 3 or 11, and it follows that . You then only have a couple of cases to check in order to conclude that a=17 and b=16.