If the product of two consecutive integers is 182, how do you find the integers?

Question

3715 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-28T23:44:22

The positive solutions are:

$floor(sqrt(182)) = 13$ and $ceil(sqrt(182)) = 14$

There are also negative solutions: $-14$ and $-13$

If the positive integers are $n$ and $n+1$ , then

$n^2 < n(n+1) < (n+1)^2$

So

$n = sqrt(n^2) < sqrt(n(n+1)) < sqrt((n+1)^2) = n+1$

Hence

$n = floor(sqrt(n(n+1)))$ and $n+1 = ceil(sqrt(n(n+1)))$