Coprime solutions to ax = b (mod n)

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985807%3A_____%2F13%3A00397165" target="_blank" >RIV/67985807:_____/13:00397165 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1515/jmc-2013-5003" target="_blank" >http://dx.doi.org/10.1515/jmc-2013-5003</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1515/jmc-2013-5003" target="_blank" >10.1515/jmc-2013-5003</a>

Result language
angličtina
Original language name
Coprime solutions to ax = b (mod n)
Original language description
It is well known that a congruence ax = b (mod n) has a solution if and only if gcd(a,n)|b, and, if the condition is satisfied, the number of incongruent solutions equals gcd(a,n). In 2010, Alomair, Clark and Poovendran proved that the congruence ax = b(mod n) has a solution coprime to n if and only if gcd(a,n) = gcd(b,n), as an auxiliary result playing a key role in a problem related to an electronic signature. In this paper we provide a concise proof of this result, together with a closed formula forthe number of incongruent solutions coprime to n as well. Moreover, a bound is presented for the probability that, for randomly chosen integer a, b, this congruence possesses at least one solution coprime to n.
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
2013
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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