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mathmath333
 one year ago
functions
mathmath333
 one year ago
functions

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mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0\(\large \color{black}{\begin{align} & f(x)=x^4+x^3+x^2+x+1,\ \ x\in \mathbb{Z}^{>1} \hspace{.33em}\\~\\ & \normalsize \text{Find remainder when }\ \large f(x^5)\ \normalsize \text{is divided by} \ \large f(x) ? \hspace{.33em}\\~\\ & a.)\ 1 \hspace{.33em}\\~\\ & b.)\ 4 \hspace{.33em}\\~\\ & c.)\ 5 \hspace{.33em}\\~\\ & d.)\ \normalsize \text{a monomial in }\ x \hspace{.33em}\\~\\ & e.)\ \normalsize \text{a polynomial in }\ x \hspace{.33em}\\~\\ \end{align}}\)

ParthKohli
 one year ago
Best ResponseYou've already chosen the best response.2Rewrite \(f(x) = \dfrac{x^51}{x1}\) and \(f(x^5) = \dfrac{x^{25}1}{x^5  1}\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Don't we need \(x<1\) for that to be true? @ParthKohli

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Oh right I'm thinking of infinite sums.

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2Notice that \(f(x) = \dfrac{x^51}{x1} \implies x^51=f(x)*(x1)\tag{1}\) \[\begin{align}f(x)&=x^4+x^3+x^2+x+1 \\~\\ \implies f(x^5)&=x^{20}+x^{15}+x^{10}+x^5+1\\~\\ &=(x^{20}1)+(x^{15}1)+(x^{10}1)+(x^51)+5\\~\\ &=(x^51)(stuff)+5\\~\\ &=f(x)*(x1)*(stuff)+5 ~~~\color{gray}{\text{(from (1))}}\\~\\ &\equiv 0+5\pmod{f(x)} \end{align}\]

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0oh u remember all things fro past cool.

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0looks very handy book

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0i will solve it within 10 years. haha

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2try these https://drive.google.com/folderview?id=0B8qeUE5SqcPAWFVaM1N5anN3S2M&usp=sharing

mathmath333
 one year ago
Best ResponseYou've already chosen the best response.0its showing "error 500"

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2try this https://drive.google.com/drive/folders/0B8qeUE5SqcPAWFVaM1N5anN3S2M

ganeshie8
 one year ago
Best ResponseYou've already chosen the best response.2it has a very good collection of olympiad textbooks
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