##
**Zentralblatt MATH**

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

**Zbl.No: ** 017.10304

**Autor: ** Erdös, Paul

**Title: ** On the sum and difference of squares of primes. II. (In English)

**Source: ** J. London Math. Soc. 12, 168-171 (1937).

**Review: ** The author proves (by Brun's method) that, for an infinity of n, the number of solutions of the equation n = p^{2}+q^{2} in primes p and q is greater than \exp**(**{c log n \over log log n}**)**. This is an improvement of the author's previous result (see Zbl 016.20103). The author also proves the theorem: Let r_{1} < r_{2} < ··· be an infinite sequence of positive integers such that for an infinity of N the number of r's less than or equal to N is greater than N\exp**(**-{c_{4} log N\over log log N} **)** with c_{4} < ^{1}/_{2} log 2. Then for an infinity of M the number of the solutions of the equation r^{2}_{j}-r^{2}_{i} = M is greater than \exp**(**{c_{2} log M\over log log M}**)**, where c_{5} depends only upon c_{4}.

**Reviewer: ** Wright (Aberdeen)

**Classif.: ** * 11N05 Distribution of primes

**Index Words: ** Number theory

© European Mathematical Society & FIZ Karlsruhe & Springer-Verlag