### 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\$

P. Anuradha Kameswari, G. Surya Kantham

#### 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\$.

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P. Anuradha Kameswari, G. Surya Kantham, 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\$, J. Math. Comput. Sci., 9 (2019), 784-795

Copyright © 2019 P. Anuradha Kameswari, G. Surya Kantham. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

J. Math. Comput. Sci.

ISSN: 1927-5307

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