<prompt> Acha px x2008 x2007 x2006 cdots x 1,na acha rx iwe salio la polynomia wakati px imegawanywa na x4x32x2x1. Tafuta salio wakati r2008 imegawanywa kwa 1000.  <response>: x4x32x2x1 x2 1x2 x 1. Tunatumia ujanibishaji wa polinomia wa Nadharia ya Mabaki ya Kichina.Hakika,px x2008 x2007 x2006 cdots x4 x3 x2 x 1 equiv x 1 pmodx2 x 1kwani xn2 x_n1 xn xn-2x2 x 1 sawa 0 pmodx2 x 1. Pia,px x2008 x2006 x2007 x2005 cdots x4 x2 x 3 x 1 sawa na 1 pmodx2 1kwa kutumia hoja sawa. Kwa hivyo px equiv x1 pmodx2 x 1, px equiv 1 pmodx2 1, na kwa CRT tuna px equiv -x2 pmodx4x32x2x1.Kisha r2008 equiv 20082 equiv 64 pmod1000. 