Some applications of linear congruence from number theory

Senad Orhani, Besim Çeko
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In this research, two distinct areas of number theory and its use in computer science are combined. In this article, an investigation was conducted on the implementation of solutions to linear congruence problems. Linear congruence is a concept implying that two integers a and b are congruent modulo m (denoted as ?? (??? ≡ ?)), if the difference between them is exactly proportional to ?. The study is important in the field of number theory and computer science which brings many benefits and efficient solutions to various problems. Therefore, the study investigates the application of linear congruence through illustrative examples, to apply number theory in finding the ISBN number, in converting decimal numbers to binary, octal, and hexadecimal, and its application in encoding and decoding messages from the field of cryptography. This section of the paper can make it easier for mathematicians to apply problems involving linear congruences, especially for those who need basic expertise in number theory. The findings of the study show that the compatibility of the book ISBN format can be checked through linear congruence. Additionally, these findings demonstrate your understanding of how to convert decimal values to binary, octal, and hexadecimal using linear congruence in a fairly comprehensive manner. Additionally, because the idea of a linear congruence system is employed in the encoding and decoding of codes for network security and other purposes, the findings of this study may be helpful to researchers working in the field of cryptography.

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