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When is the sum of first $n$ numbers equal to the sum of the next $k$ numbers?
When is the sum $1+2+\cdots + n = (n+1) + (n+2) + \cdots +(n+k)$?
The easiest solution $(n,k)$ is $(2,1)$. For example, $1+2 = 3$. Do any others exist?
Roots of $(n+k)^2 + (n+k) = 2n^2 +2n$ give ...
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