## On Sums With Small Prime Factors

### Author: Gabor Sarkozy

ABSTRACT

Improving the existing bounds on a problem of P. Erdos, that can be viewed as the conversion of the Goldbach problem, we prove the following: Let epsilon > 0 be fixed. Every integer N>N_0 (epsilon ) can be written in the form N = n_1 + n_2 + n_3 where the greatest prime factor of n_1 n_2 n_3 is <= exp ( (\sqrt{3/2} + epsilon) ( log N log log N)^{1/2} ). We also show that the same statement is not true with ( log N )^{{3/2} - epsilon}.

Paper only.