Application of Fermat’s Little Theorem in Congruence Relation Modulo n
Journal Title: International Journal of Innovative Research in Computer Science and Technology - Year 2022, Vol 10, Issue 2
Abstract
According to Fermat's little theorem, for any p is a prime integer and gcdx,p=1, then the congruence xp-1≡1mod n is true, if we remove the restriction that gcdx,p=1, we may declarexp-1≡xmod p. For every integer x. Euler extended Fermat's Theorem as follows: if gcdx,p=1,then,where xÏ•n≡1mod n.Ï• is Euler's phi-function. Euler's theorem cannot be implemented for any every integers x in the same manners as Fermat’s theorem works; that is, the congruence xÏ•n+1≡xmod n is not always true. In this paper, we discussed the validation of congruence xÏ•n+1≡xmod n.
Authors and Affiliations
S. P. Behera, J. K. Pati, S. K. Patra, P. K. Raut
Keywords
Related Articles
- EP ID EP746537
- DOI 10.55524/ijircst.2022.10.2.2
- Views 5
- Downloads 0
IoT Based Smart Alert Network Security System Using Machine Learning
The increasing security threats in public places such as airports, train stations, and shopping malls require the development of smart security systems that can detect potential threats and provide timely alerts to secur...
Investigative Study on the Properties of Hollow Concrete Blocks
The utilization of workmanship structures is as yet broad all through the world. Hollow concrete blocks have supplanted customary bricks in late development as a result of the upsides of higher bearing limit, farmland in...
Hybrid Active Power Filter for Power Quality Improvement
A Deadbeat current controller for an LC-coupling hybrid active power filter is proposed, which can track with the reference compensation current with low steady- state error and fast dynamic response. Moreover, it can le...
Adaptation, Machine Learning, and the Immune System: A Review Paper
The immunologic system is a critical dynamic system whose goal it is to detect and eliminate foreign matter. In order to do any of this, this must be able to tell the difference across much particles (or antigens) and th...
Research on Decryption Methodologies and Key Aggregate Searchable Encryption for Data Security Storage in Cloud
Numerous firm’s architectures management of data guarantees substantially alter method, gain access to maintain private commercial business. Occur additional facts protection problems. Existing statistics safety methods...