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AM is two more than GM

Source:

January 5, 2007

quadraticsAMCAIMEalgebraquadratic formula

Problem Statement

For how many ordered pairs

(x,y)

of integers is it true that

0<x<y<10^{6}

and that the arithmetic mean of

x

and

y

is exactly

2

more than the geometric mean of

x

and

y?

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