1.3.3 Sum of Consecutive Squares

Usually when approached with this problem, one of the squares ends in 5 making the squaring of the number relatively trivial. You want to use the approach of factoring to help aid in these problems. For example:

$$35^2 + 36^2 = 35^2 + (35 + 1)^2$$ $$= 2 \cdot 35^2 + 2 \cdot 35 + 1^2$$ $$= 2 \cdot 1225 + 70 + 1 = 2521$$

This is a brute force technique, however, it is a lot better than squaring both of the numbers and then adding them together (which you can get lost very easily doing that).

Problem Set 1.3.3

Here are some more practice problems to familiarize yourself with this procedure.