MathDB

4

Part of 1986 Poland - Second Round

Problems(1)

x + y = perfext square if 1/x +1/y=1/z

Source: Polish MO Recond Round 1986 p4

9/9/2024
Natural numbers x,y,z x, y, z whose greatest common divisor is equal to 1 satisfy the equation 1x+1y=1z\frac{1}{x} + \frac{1}{y} = \frac{1}{z} Prove that x+y x + y is the square of a natural number.
number theoryPerfect SquarediophantineDiophantine equation