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

PEN J Problems, 14
Tags: Divisor Functions , pen , imo shortlist 2001
Find all positive integers $n$ such that ${d(n)}^{3} =4n$.

2001 IMO Shortlist, 5
Tags: inequalities , algebra , recurrence relation , equation , Integer sequence , IMO Shortlist , imo shortlist 2001
Find all positive integers $a_1, a_2, \ldots, a_n$ such that \[ \frac{99}{100} = \frac{a_0}{a_1} + \frac{a_1}{a_2} + \cdots + \frac{a_{n-1}}{a_n}, \] where $a_0 = 1$ and $(a_{k+1}-1)a_{k-1} \geq a_k^2(a_k - 1)$ for $k = 1,2,\ldots,n-1$.