We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Dio...We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp.展开更多
This paper deals with the security of stock market transactions within financial markets, particularly that of the West African Economic and Monetary Union (UEMOA). The confidentiality and integrity of sensitive data ...This paper deals with the security of stock market transactions within financial markets, particularly that of the West African Economic and Monetary Union (UEMOA). The confidentiality and integrity of sensitive data in the stock market being crucial, the implementation of robust systems which guarantee trust between the different actors is essential. We therefore proposed, after analyzing the limits of several security approaches in the literature, an architecture based on blockchain technology making it possible to both identify and reduce the vulnerabilities linked to the design, implementation work or the use of web applications used for transactions. Our proposal makes it possible, thanks to two-factor authentication via the Blockchain, to strengthen the security of investors’ accounts and the automated recording of transactions in the Blockchain while guaranteeing the integrity of stock market operations. It also provides an application vulnerability report. To validate our approach, we compared our results to those of three other security tools, at the level of different metrics. Our approach achieved the best performance in each case.展开更多
文摘We analyse the Diophantine equation of Fermat xp yp = zp with p > 2 a prime, x, y, z positive nonzero integers. We consider the hypothetical solution (a, b, c) of previous equation. We use Fermat main divisors, Diophantine remainders of (a, b, c), an asymptotic approach based on Balzano Weierstrass Analysis Theorem as tools. We construct convergent infinite sequences and establish asymptotic results including the following surprising one. If z y = 1 then there exists a tight bound N such that, for all prime exponents p > N , we have xp yp zp.
文摘This paper deals with the security of stock market transactions within financial markets, particularly that of the West African Economic and Monetary Union (UEMOA). The confidentiality and integrity of sensitive data in the stock market being crucial, the implementation of robust systems which guarantee trust between the different actors is essential. We therefore proposed, after analyzing the limits of several security approaches in the literature, an architecture based on blockchain technology making it possible to both identify and reduce the vulnerabilities linked to the design, implementation work or the use of web applications used for transactions. Our proposal makes it possible, thanks to two-factor authentication via the Blockchain, to strengthen the security of investors’ accounts and the automated recording of transactions in the Blockchain while guaranteeing the integrity of stock market operations. It also provides an application vulnerability report. To validate our approach, we compared our results to those of three other security tools, at the level of different metrics. Our approach achieved the best performance in each case.
