Start with x5y3=x8y5x5y3=x8y5 and multiply it with x−5x−5 to the left and with y−3y−3 to the right. We get e=x3y2e=x3y2 and therefore x3y2=x5y3=ex3y2=x5y3=e By the same way we get to e=x2y=x3ye=x2y=x3y and again this yields x=ex=e Replacing in the initial identity we get y3=y5=ey3=y5=e and through the same approach we get to y=e