5

Part of 1996 Dutch Mathematical Olympiad

Problems(1)

1/x+1/y=1/z , gcd (x,y,z)=1 then (x + y) is a perfect square

Source: Dutch NMO 1996 p5

For the positive integers

x , y

z

\frac{1}{x}+\frac{1}{y}=\frac{1}{z}

. Prove that if the three numbers

x , y,

z

have no common divisor greater than

1

x + y

is the square of an integer.

number theorygreatest common divisorPerfect Square