# If the sum of two consecutive integers is less than 83, how do you find the pair of integers with the greatest sum?

##### 1 Answer

Two integers can only add to become another integer. The greatest integer less than

However, you can't have two *consecutive integers* adding up to give an even number, so we're going to have to pick the greatest *odd* number that's smaller than

So we are looking for two consecutive integers that add up to

To do this, we can add them and set them equal to

And that is good information, by we are looking for the biggest odd number that's smaller than