MathDB

a=\frac{x_1^2+x_2^2+... + x_n^ 2}{x_1x_2 ... x_n}

Source: Argentina 2003 OMA L3 p3

May 12, 2024

algebranumber theory

Problem Statement

Let

a\geq 4

be a positive integer. Determine the smallest value of

n\geq 5

n\neq a

, such that

a

can be represented in the form

a=\frac{x_1^2+x_2^2+\cdots + x_n^ 2}{x_1x_2\cdots x_n}

for a suitable choice of the

n

positive integers

x_1,x_2,\ldots ,x_n