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 = p2+q2 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 r1 < r2 < ··· 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(-{c4 log N\over log log N} ) with c4 < 1/2 log 2. Then for an infinity of M the number of the solutions of the equation r2j-r2i = M is greater than \exp({c2 log M\over log log M}), where c5 depends only upon c4.
Reviewer:  Wright (Aberdeen)
Classif.:  * 11N05 Distribution of primes
Index Words:  Number theory

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