Question

In how many different ways you can write 15 as the difference of the squares of two natural numbers?

Answer 1

The factors of 15 are 1, 3, 5 and 15.

We can write 15 as:

15 = 1 × 15

= (8 − 7) (8 + 7) {x² − y² = (x − y) (x + y)}

= 8² − 7²

So, 15 can be written as the difference of the squares of 8 and 7.

15 = 3 × 5

= (4 − 1) (4 + 1) {x² − y² = (x − y) (x + y)}

= 4² − 1²

So, 15 can be written as the difference of the squares of 4 and 1.

Thus, there are two ways to write 15 as the difference of the squares of two natural numbers.