A constructive proof of scherk's theorem on the representation of primes

All of the known proofs of Scherk's theorem are existence proofs which are non-constructive, and don't provide a procedure for choosing the signs in Scherk's representation of primes. This paper presents a constructive proof of Scherk's theorem based on an explicit algorithm for...

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Bibliographic Details
Published in:International journal of computer mathematics Vol. 50; no. 3-4; pp. 125 - 130
Main Authors: Shapiro, Jacob, Waxman, Jerry
Format: Journal Article
Language:English
Published: Abingdon Gordon and Breach Science Publishers S.A 01.01.1994
Taylor and Francis
Subjects:
Algebra
Algorithmics. Computability. Computer arithmetics
Algorithms in number theory
Applied sciences
Computer science; control theory; systems
Discrete mathematics
Exact sciences and technology
F.2
G.2
Logic and foundations
Mathematical logic, foundations, set theory
Mathematics
Number theory
Problem complexity
Recursion theory
representation of prime numbers
Scherk's theorem
Sciences and techniques of general use
Theoretical computing
Complexity class
Algorithm
Prime number
Number theory
ISSN:0020-7160, 1029-0265
Online Access:Get full text
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Summary:All of the known proofs of Scherk's theorem are existence proofs which are non-constructive, and don't provide a procedure for choosing the signs in Scherk's representation of primes. This paper presents a constructive proof of Scherk's theorem based on an explicit algorithm for choosing the signs in time 0(n).
ISSN:0020-7160
1029-0265
DOI:10.1080/00207169408804249