New Solvability Conditions for Congruence $axequiv bpmod n$

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F15%3A00456640" target="_blank" >RIV/67985807:_____/15:00456640 - isvavai.cz</a>
Result on the web
<a href="http://tatra.mat.savba.sk/paper.php?id_paper=1263" target="_blank" >http://tatra.mat.savba.sk/paper.php?id_paper=1263</a>
DOI - Digital Object Identifier
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Result language
angličtina
Original language name
New Solvability Conditions for Congruence $axequiv bpmod n$
Original language description
K.Bibak et al. [arXiv:1503.01806v1 [math.NT], March 5 2015] proved that congruence ax=b (mod n) has a solution x with gcd(x,n)=t if and only if gcd(a,n/t)=gcd(b/t,n/t) thereby generalizing the result for t=1 proved by B.Alomair et al. [J. Math. Cryptol.4 (2010), 121-148] and O.Grošek et al. [ibid. 7 (2013), 217-224]. We show that this generalized result for arbitrary t follows from that for t=1 proved in the later papers. Then we shall analyze this result from the point of view of a weaker condition that gcd(a,n/t) only divides gcd(b/t,n/t). We prove that given integers n>=1,a,b and t>=1, congruence ax=b (mod n) has a solution x with t dividing gcd(x,n) if and only if gcd(a,n/t) divides gcd(b/t,n/t).
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP201%2F12%2F2351" target="_blank" >GAP201/12/2351: Distribution and metric properties of number sequences and their applications</a><br>
Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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