A property of polynomials

$A P R O P E R T Y O F P O L Y N O M I A L S$

Let $f(x)$ be a polynomial in $x$ where $x$ $a n d t h e c o e f f i c i e n t s$ $a)areintegers,$ b) $\\hskip 36.135pt\\,$ x $i s a s q u a r e m a t r i x a n d$ k ${\\hskip 0.0pt.5in}\\ isanaturalnumber.$ $T h e p r o p e r t y :$ $f(x+k*f(x))iscongruentto$ 0 $m o d$ f(x) $.$ Proof:

\\hskip 36.135pt\\$\\hskip 36.135pt\\ Thereisnolossofgeneralityintakingk=1.%ByTaylor^{\\prime}stheoremweget\\par f(x+f(x))=f(x)+f(x)f^{\\prime}(x)+(f(x)^{2}%)/2f^{\\prime\\prime}(x)+(f(x)^{3})/3!f^{\\prime\\prime\\prime}(x)....=f(x){1+f^{%\\prime}(x)+f(x)/2*f^{\\prime\\prime}(x)+f(x)^{2}/3!..}i.e.f(x+f(x))iscongruentto%0(mod(f(x))).\\par\\begin{flushright}\\begin{tabular}[]{|ll|}\\hline Title&A %property of polynomials\\\\Canonical name&APropertyOfPolynomials\\\\Date of creation&2013-03-22 19:34:45\\\\Last modified on&2013-03-22 19:34:45\\\\Owner&akdevaraj (13230)\\\\Last modified by&akdevaraj (13230)\\\umerical id&17\\\\Author&akdevaraj (13230)\\\\Entry type&Definition\\\\Classification&msc 11C08\\\\\\hline\\end{tabular}\\end{flushright}\\end{document}