On 4/n=1/x + 1/y + 1/z and Iwaniec′ Half Dimensional Sieve Original Research Article

A well-known conjecture says that for any integer n > 1 the equation 4/n = 1/x + 1/y + 1/z has a solution in positive integers x, y, and z. By use of sieve methods we prove some asymptotic formulae and lower bounds for certain exceptional sets related to this problem.