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help reqd in editing

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Would be grateful for receiving for Tex editing of the article below:

1 A PROPERTY OF POLYNOMIALS

Let f(x)fxf(x) be a polynomial in xxx where xxx and the coefficients a(Z)aZa\in\mathbb{(}Z) and bxbxbx is a square re k(Z)kZk\in\mathbb{(}Z) .

Proof: There is no loss of generality in taking k=1k1k=1. By Taylor’s theorem we get

f(x+f(x))=f(x)+f(x)f(x)+(f(x)2)/2f′′(x)+(f(x)3)/3!f′′′(x).fxfxfxfxsuperscriptfnormal-′xfsuperscriptx22superscriptf′′xfsuperscriptx33superscriptf′′′xnormal-…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(x)+f(x)/2*f′′(x)+f(x)2/3!..)fragmentsffragmentsnormal-(xnormal-)fragmentsnormal-(1superscriptfnormal-′fragmentsnormal-(xnormal-)ffragmentsnormal-(xnormal-)2superscriptf′′fragmentsnormal-(xnormal-)fsuperscriptfragmentsnormal-(xnormal-)23normal-.normal-.normal-)=f(x)(1+f^{{\prime}}(x)+f(x)/2*f^{{\prime\prime}}(x)+f(x)^{2}/3!..)

i.e. f(x+f(x))fxfxf(x+f(x)) is 0(mod(f(x)).fragments0fragmentsnormal-(modulofragmentsnormal-(ffragmentsnormal-(xnormal-)normal-)normal-.\equiv 0(\mod(f(x)).


I added some LaTeX markup to your post, but I’m not entirely sure what the request is. The way you set up the question it’s not clear what role aaa, bbb, and kkk play, for example.

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