## DIMACS TR: 93-80

## 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.

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