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

Tags were heavily modified to better represent problems.

AND:
OR:
NO:

Found problems: 2

2013 Math Prize For Girls Problems, 19
Tags: relatively prime , mew , number theory
If $n$ is a positive integer, let $\phi(n)$ be the number of positive integers less than or equal to $n$ that are relatively prime to $n$. Compute the value of the infinite sum \[ \sum_{n=1}^\infty \frac{\phi(n) 2^n}{9^n - 2^n} \, . \]

2022 Math Prize for Girls Olympiad, 2
Tags: mew
Determine, with proof, whether or not there exists a [i]non-isosceles[/i] trapezoid $ABCD$ such that the lengths $AC$ and $BD$ both lie in the set $\{ DA+AB, AB+BC, BC+CD, CD+DA, AB+CD, BC+DA \}$.