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math.NT2026
Some Methods to Solve the Diophantine Equation ay^2=b(x^k-c^k)
Xiaodong Zhuang, Nikos E. Mastorakis
The solution of the Diophantine equation ay^2=b(x^k-c^k) is studied in different cases of k. Methods are proposed for different cases of k, which are convenient for computer algori…
math.NT2026★ 2 cited
Optimization of Quadratic Sieve Algorithm Implementation for Large Integer Factorization
Zihan Guan, Xiaodong Zhuang, Nikos E. Mastorakis
The quadratic sieve method is a core tool in number theory. In this paper, we present two optimization methods for the Quadratic Sieve algorithm. In the sieving process, the origin…
math.NT2026
Methods to Find Integer Points on the Elliptic Curve of Factorizable Polynomial Equation
Xiaodong Zhuang, Nikos E. Mastorakis
As a valuable theoretical and application problem, the integer points on two types of elliptic curve y^2=(x-a)(x-b)(x-c) and y^2 = (x-a)(x^2+ax+b) are studied. By using elementary…