Math CentralQuandaries & Queries


Question from Adeeb,

Find two consecutive odd positive integers, sum of whose square is 290.

Hi Adeeb,

I can help get you started.

Any odd integer is one less than an even number. Thus the smaller of your two odd numbers is one less that an even number.This even number is divisible by 2 so it can be written $2 \times n$ for some integer $n.$ Thus the smallest of your two odd integers is $2n - 1.$ The next integer is $2 n$ which is even and the next integer is $2n + 1.$ Hence the two consecutive odd integers are $2n - 1$ and $2n + 1.$ The sum of their squares is 290. Solve for $n.$

Make sure that you verify your answer.


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