An Elementary Method for Estimating Error Terms in Additive Number Theory

An asymptotic formula in additive number theory

1 . Introduction . In his paper [1], Erdös introduced the sequences of positive integers b 1 < b, < . . ., with (b ;, bj ) = 1, for i ~A j, and 'bi 1 < oo . With any such arbitrary sequence of integers, he associated the sequence {di} of all positive integers not divisible by any bj , and he showed that if b1 > 2, there exists a 0 < 1 (independent of the sequence {b i }) such that d i 1 di < d°...

An Unsolvable Problem of Elementary Number Theory

Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at http://www.jstor.org/about/terms.html. JSTOR's Terms and Conditions of Use provides, in part, that unless you have obtained prior permission, you may not download an entire issue of a journal or multiple copies of articles, and you may use content in the JSTOR archive only for your perso...

On a New Method in Elementary Number Theory Which Leads to An Elementary Proof of the Prime Number Theorem.

Elementary Number Theory

Elementary number theory

The division relation plays a prominent role throughout this note, and so, we start by presenting some of its basic properties and their relation to addition and multiplication. First, it is re exive because multiplication has a unit (i.e., m= 1×m) and it is transitive, since multiplication is associative. It is also (almost) preserved by linear combination because multiplication distributes ov...