MathDB

very beautiful problem

Source: Romanian IMO Team Selection Test TST 1996, problem 8

September 6, 2005

inequalitiesnumber theory unsolvednumber theory

Problem Statement

Let

p_1,p_2,\ldots,p_k

be the distinct prime divisors of

n

and let

a_n=\frac {1}{p_1}+\frac {1}{p_2}+\cdots+\frac {1}{p_k}

for

n\geq 2

. Show that for every positive integer

N\geq 2

the following inequality holds:

\sum_{k=2}^{N} a_2a_3 \cdots a_k <1

Laurentiu Panaitopol