BdMO National Secondary 2007#7
Posted: Sat Feb 23, 2019 9:13 am
Find the smallest positive integer $n>1$, such that $\sqrt{1+2+3+...+n}$ is an integer.$(n<10)$.
Answer: $\fbox 8$
$\sqrt{1+2+3+4+5+6+7+8}\Rightarrow \sqrt{36}\Rightarrow 6$
And $1<8<10$.
So our desired $n=8$.