Some results in number theory, I
نویسندگان
چکیده
منابع مشابه
Some results of number theory
This is a collection of formalized proofs of many results of number theory. The proofs of the Chinese Remainder Theorem and Wilson’s Theorem are due to Rasmussen. The proof of Gauss’s law of quadratic reciprocity is due to Avigad, Gray and Kramer. Proofs can be found in most introductory number theory textbooks; Goldman’s The Queen of Mathematics: a Historically Motivated Guide to Number Theory...
متن کاملSome Problems and Results in Number Theory
During my very long life I published many papers of similar title . Here I want to discuss some of my favorite problems many of which go back 50 years and which I hope are still alive and will outlive me . Recently Graham and I published a book entitled "Old and new problems and results in combinatorial number theory" Monographic N ° 28 de L'Enseignement Mathématique, Univ . de Genéve . This bo...
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Let 0 <a 1 <a2< . . . be any infinite sequence of integers . Denote by N(ai , n) the number of ai S n . I conjectured that to every sequence ai there corresponds a sequence b ; of density 0 (i .e ., such that lim n (1/n)N(b;, n)=0) so that every sufficiently large integer is of the form a i +b;. Lorentz 2 in a recent paper proved this conjecture ; in fact, he showed that there exists a sequence...
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Article history: Received 6 March 2015 Received in revised form 18 July 2015 Accepted 19 July 2015 Available online 10 September 2015 Communicated by David Goss
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C.F. Gauss [Gaus1] [Gaus2] showed that the the number of lattice points in circles is the area, πt , up to a tolerance of order at most the circumference, i.e. the square root, O( √ t) . Sierpinski in 1904, following work of Voronoi [Vor] on the Dirichlet Divisor Problem, lowered the exponent in Gauss’s result to 1/3 [Sierp1] [Sierp2]. Further improvements that have been obtained will be descri...
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ژورنال
عنوان ژورنال: Acta Arithmetica
سال: 1979
ISSN: 0065-1036,1730-6264
DOI: 10.4064/aa-35-4-367-371