# The product of two consecutive odd integers is 899. How do you find the integers?

Dec 27, 2016

899 is just 1 less than 900. And 900 is the square of 30. And 1 is the square of 1. So 899 is the difference of two squares.

#### Explanation:

We have a special product here, of the form:
$\left(A - B\right) \left(A + B\right) = {A}^{2} - {B}^{2}$

If we take $30 \mathmr{and} 1$ for $A \mathmr{and} B$:
$\left(30 - 1\right) \left(30 + 1\right) = {30}^{2} - {1}^{2} = 900 - 1 = 899$ BINGO!

So the answer is $29 \mathmr{and} 31$

Note : of course $- 29 \mathmr{and} - 31$ also count as a solution.