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

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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)))#