3

Part of 2003 Argentina National Olympiad

Problems(1)

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

Source: Argentina 2003 OMA L3 p3

a\geq 4

be a positive integer. Determine the smallest value of

n\geq 5

n\neq a

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

algebranumber theory