This website contains problems from math contests. Problems and corresponding tags were obtained from the Art of Problem Solving website.

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Found problems: 2

2015 Thailand TSTST, 2
Tags: quadratic mean , number theory
Determine the least integer $n > 1$ such that the quadratic mean of the first $n$ positive integers is an integer. [i]Note: the quadratic mean of $a_1, a_2, \dots , a_n$ is defined to be $\sqrt{\frac{a_1^2+a_2^2+\cdots+a_n^2}{n}}$.[/i]

2024 Brazil Cono Sur TST, 1
Tags: quadratic mean , inequalities
The sum of $2025$ non-negative real numbers is $1$. Prove that they can be organized in a circle in such a way that the sum of all the $2025$ products of pairs of neighbouring numbers isn't greater than $\frac{1}{2025}$.