Sieving polynomial for factorization of numbers of the form n = m^5 + a_4m^4 + a_3m^3 + a_2m^2 + a_1m + a_0 for a_i << m

Abstract

In the process of factorization of general integers in 1998 Zhang developed a method which can factor integers of the form $n = m^3+a_2m^2+a_1m+a_0$ for $a_i<<m$ by considering $x = b_2m^2+b_1m+b_0$ and as in 2002 Eric Landquist [10] generalized the method for numbers of the form $n= m^5+a_0$. In this paper going in the lines of Eric and using solutions of quadratic equation $ax^2+bxy+cy^2 = z^2$ we proposed some parametrization for $b_i$'s that are non trivial by considering $x = b_3m^3+b_2m^2+b_1m+b_0$ and obtained sieving polynomial for factoring of the numbers of the form $n = m^5+a_4m^4+a_3m^3+a_2m^2+a_1m+a_0$  with $a_i<<m$.