sqrt

AntonVrba

[tex]
{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\\
[/tex]

Jimmy Snyder

This is what I think the post means:

If [itex]{B_n} = {\sqrt{\sum _{y=1}^{n}\sum _{z=1}^{y}{z^2}}}[/itex], then here are some values of [itex]n[/itex] for which [itex]B_{n}[/itex] is an integer.

[itex]{B_1} = 1[/itex]
[itex]{B_6} = 14[/itex]
[itex]{B_{25}} = 195[/itex]

The largest [itex]n < {10}^{10}[/itex] for which [itex]B_{n}[/itex] is an integer is 9863382150

[itex]B_{9863382150} = 28084137899285228670[/itex]


But there is no question here. I don't know any method other than brute force to prove the last statement.