##
**Zentralblatt MATH**

**Publications of (and about) Paul Erdös**

**Zbl.No: ** 214.30603

**Autor: ** Erdös, Paul

**Title: ** Some applications of graph theory to number theory (In English)

**Source: ** Proc. 2nd Chapel Hill Conf. Combin. Math. Appl., Univ. North Carolina 1970, 136-145 (1970).

**Review: ** [For the entire collection see Zbl 208.00201.]

Several applications of graph theory to number theory are discussed mostly without proofs. The following result is proved in detail: Let a_{1} < ... < a_{k} \leq x, k > \pi (x) be a sequence of integers. Denote by f(k,x) the smallest integer r so that there always are r primes p_{1}, ... ,p_{r} for which more than r a's are of the form **prod** ^{r}_{i = 1}p^{\alphai}_{i}. The author and Straus proved f(\pi (x)+1,x) = (4+o(1)){x^{ ½} \over log x}. A good estimate is given for f(k,x) if k = cx.

**Classif.: ** * 11B75 Combinatorial number theory

11N99 Multiplicative number theory

**Citations: ** Zbl 208.00201(EA)

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag