The tutor gives a few integer solutions to a²+b²=c².

All-integer solutions to a²+b²=c² are called Pythagorean triples. They are comparativeley rare. Here are three sets I know:

3,4,5

5,12,13

8,15,17

From the sets above, infinitely more can be generated: multiplying all three of a set by the same number gives another one. Therefore, some additional Pythagorean triples are

6,8,10 and 9,12,15 (based on 3,4,5)

10,24,26 (based on 5,12,13)

80,150,170 (based on 8,15,17)

I’ll be talking more about Pythagorean triples.

Source:

Dudley, Underwood. Elementary Number Theory, 2nd Ed. New York: W H Freeman
   and Company, 1978.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.