16

Part of 2016 India PRMO

Problems(1)

2016 preRMO p16, average of arithmetic and geometric mean, is perfect square

Source:

For positive real numbers

x

y

, define their special mean to be average of their arithmetic and geometric means. Find the total number of pairs of integers

(x, y)

x \le y

, from the set of numbers

\{1,2,...,2016\}

, such that the special mean of

x

y

is a perfect square.

algebrageometric meanarithmetic meanPerfect Squarenumber theory