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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

An efficient algorithmic solution of the Diophantine equation $ u\sp{2}+5v\sp{2}=m$


Author: Peter Wilker
Journal: Math. Comp. 35 (1980), 1347-1352
MSC: Primary 10B05; Secondary 10-04, 10A25
MathSciNet review: 583512
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Abstract: The determination of irreducible elements of the domain $ Z[\sqrt { - 5} ]$ requires the solution of the Diophantine equation $ {u^2} + 5{v^2} = m$, where m represents certain primes or products of two primes. An algorithm of order $ \log m$ is given for the solution of the equation.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0583512-5
PII: S 0025-5718(1980)0583512-5
Article copyright: © Copyright 1980 American Mathematical Society