## sqrt

$${A_n}={\sqrt{\sum _{z=1}^{n}{z^2}}} \\ {A_1}=1 \\ {A_{24}}=70\IndentingNewLine \IndentingNewLine \\ {B_n}={\sqrt{\sum _{y=1}^{n}\sum _{z=1}^{y}{z^2}}} \\ {B_1}=\multsp 1 \\ {B_6}=14 \\ {B_{25}}=195 \\ \Mvariable{the}\multsp \Mvariable{largest}\multsp n\multsp <{{10}^{10}}\multsp \Mvariable{is} \\ {B_{9863382150}}=28084137899285228670\\$$
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 Blog Entries: 1 Recognitions: Gold Member This is what I think the post means: If ${B_n} = {\sqrt{\sum _{y=1}^{n}\sum _{z=1}^{y}{z^2}}}$, then here are some values of $n$ for which $B_{n}$ is an integer. ${B_1} = 1$ ${B_6} = 14$ ${B_{25}} = 195$ The largest $n < {10}^{10}$ for which $B_{n}$ is an integer is 9863382150 $B_{9863382150} = 28084137899285228670$ But there is no question here. I don't know any method other than brute force to prove the last statement.