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Old 15th February 2012, 01:28 PM   #1 (permalink)
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Sch quiz help

Set by my sch.


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Old 17th February 2012, 10:49 AM   #2 (permalink)
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Re: Sch quiz help

Here are the workings;



Hope it helps. Peace.


Last edited by whitecorp; 17th February 2012 at 10:50 AM.
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Old 17th February 2012, 11:01 AM   #3 (permalink)
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Re: Sch quiz help

Wow whitecorp, thats chim

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Old 17th February 2012, 11:24 AM   #4 (permalink)
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Re: Sch quiz help

You can decipher the general template by using lower order polynomials divided by x^2-2x+1; for example x^5 + 1 or x^9 +1 . You should be able to identify a certain pattern rather quickly and extend this to x^n +1 , where n is any positive integer. Peace.

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Old 17th February 2012, 10:18 PM   #5 (permalink)
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Re: Sch quiz help

thanks. I learned a new skill o.o (++ food voucher! hungry hungry - if i am the first 3 though... )

i was puzzled by your solution till you said find a general pattern using smaller values of n.

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Old 17th February 2012, 10:23 PM   #6 (permalink)
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Re: Sch quiz help

No problem. Hope you will win the voucher. Peace.

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Old 18th February 2012, 01:55 AM   #7 (permalink)
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Re: Sch quiz help

Took me really quite some time... Does not require any trend.

x⁹⁹⁹+1
=(x⁹⁹⁹-1)+2
=(x-1)(x⁹⁹⁸+x⁹⁹⁷+...+-1+2)+2
=(x-1)(x⁹⁹⁷+x⁹⁹⁶+...+2)+(x-1)(x⁹⁹⁷+x⁹⁹⁶+...+1)+2
=(x⁹⁹⁷+x⁹⁹⁶+...+2)x-(x⁹⁹⁷+x⁹⁹⁶+...+2)+2+(x-1)(x⁹⁹⁷+x⁹⁹⁶+...+1)
=P(x)(x-1)+Ax+B
x=1,
1999x-1999-2+0=0+Ax+B
∴remainder = 1999x-1997


Last edited by Icystrike; 18th February 2012 at 01:56 AM.
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