Find all $x$ so $\dfrac{1^2+2^2+\cdots+x^2}{x}$ is a perfect square... Clearly 1 is solution, but I have to show that there is an infinity... I see that this happens when the numbers $1,2,...,x$ have a whole quadratic root. Am I on the right road?
Find all $x$ so $\dfrac{1^2+2^2+\cdots+x^2}{x}$ is a perfect square...
Clearly 1 is solution, but I have to show that there is an infinity... I see that this happens when the numbers $1,2,...,x$ have a whole quadratic root. Am I on the right road?
