Zobrazeno 1 - 7
of 7
pro vyhledávání: '"Gaussian moat"'
Publikováno v:
Communications in Computer and Information Science ISBN: 9783030617011
ICAI
ICAI
In the year 1832, the well known German mathematician Carl Friedrich Gauss proposed the set of Gaussian integers, which corresponds to those complex numbers whose real and imaginary parts are integer numbers. A few years later, Gaussian primes were d
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::ec331d69aa182f4c661e69e0ef20ab0a
https://doi.org/10.1007/978-3-030-61702-8_33
https://doi.org/10.1007/978-3-030-61702-8_33
Autor:
Akshaa Vatwani
Publikováno v:
Journal of Number Theory. 171:449-473
We show that there are infinitely many distinct rational primes of the form p 1 = a 2 + b 2 and p 2 = a 2 + ( b + h ) 2 , with a , b , h integers, such that | h | ≤ 246 . We do this by viewing a Gaussian prime c + d i as a lattice point ( c , d ) i
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::bd94a42b0895bcfeb3527f8c9c74e1f6
https://doi.org/10.1016/j.jnt.2016.07.008
https://doi.org/10.1016/j.jnt.2016.07.008
Autor:
Po-Ru Loh
Publikováno v:
The American Mathematical Monthly. 114:142-151
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::45711bfd764543ddfbd6e781b2eddc79
https://doi.org/10.1080/00029890.2007.11920399
https://doi.org/10.1080/00029890.2007.11920399
Publikováno v:
2015 International Conference on Control Communication & Computing India (ICCC).
This paper is primarily concerned with the definition of perfect integers in the Gaussian plane and then testing their existence with the help of number theoretic algorithms and other computational tools. Here, we deal with Gaussian primes, their pri
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::a5fbcb884a081c671c9c49a30f4edb3e
https://doi.org/10.1109/iccc.2015.7432987
https://doi.org/10.1109/iccc.2015.7432987
Autor:
Nobuyuki Tsuchimura
Publikováno v:
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences. :1267-1273
"Can one walk to infinity on Gaussian primes taking steps of bounded length?" We adopted computational techniques to probe into this open problem. We propose an efficient method to search for the farthest point reachable from the origin, which can be
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::97eb89d9180ba249ff88b2c3be624157
https://doi.org/10.1093/ietfec/e88-a.5.1267
https://doi.org/10.1093/ietfec/e88-a.5.1267
Autor:
H. M. Stark, Ellen Gethner
Publikováno v:
Experiment. Math. 6, iss. 4 (1997), 289-292
A question of Gordon, mistakenly attributed to Erdős, asks if one can start at the origin and walk from there to infinity on Gaussian primes in steps of bounded length. We conjecture that one can start anywhere and the answer is still no. We introdu
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::b019981f06e09af6c49443de97a02df9
https://doi.org/10.1080/10586458.1997.10504616
https://doi.org/10.1080/10586458.1997.10504616
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