2018 UNCO Math Contest II Problems/Problem 11

Problem

(a) Find an integer $n > 1$ for which $1 + 2 + \ldots + n^2$ is a perfect square. (b) Show that there are infinitely many integers $n > 1$ that have the property that $1 + 2 + \ldots + n^2$ is a perfect square, and determine at least three more examples of such $n$. Hint: There is one approach that uses the result of a previous problem on this contest.

Solution

$7$ (Other acceptable answers are $41, 239, 1393, 8119$, and, in general, anything generated by the formula in part b. The answer students are most likely to give is $7$

See also

2018 UNCO Math Contest II (ProblemsAnswer KeyResources)
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