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 August 26th, 2012, 05:03 AM #1 Newbie   Joined: May 2012 Posts: 6 Thanks: 0 Demonstration help Prove that the 1979 first algarisms after the comma, of the number $(6+\sqrt{35})^{1980}$, are all algarisms 9. *Sorry, maybe there's a grammar error, this is a direct translation from portuguese.
 August 26th, 2012, 05:40 AM #2 Global Moderator     Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms Re: Demonstration help I don't know the word "algarisms".
 August 26th, 2012, 05:59 AM #3 Newbie   Joined: May 2012 Posts: 6 Thanks: 0 Re: Demonstration help Sorry, edit: Prove that the 1979 first digits after the comma, of the number , are all algarisms 9.
 August 26th, 2012, 06:01 AM #4 Newbie   Joined: May 2012 Posts: 6 Thanks: 0 Re: Demonstration help Prove that the 1979 first digits after the comma, of the number $(6+\sqrt35)^{1980}$, are all algarisms 9. Why can't I edit my posts?
 August 26th, 2012, 06:05 AM #5 Math Team     Joined: Mar 2012 From: India, West Bengal Posts: 3,871 Thanks: 86 Math Focus: Number Theory Re: Demonstration help "algarisms" is not an english word.
August 26th, 2012, 06:08 AM   #6
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Re: Demonstration help

Quote:
 Originally Posted by mathbalarka "algarisms" is not an english word.
Yep, i forgot to change the second one. Sorry, again...

Prove that the 1979 first digits after the comma, of the number $(6+\sqrt{35})^{1980}$ , are all algarisms 9.

 August 26th, 2012, 06:10 AM #7 Newbie   Joined: May 2012 Posts: 6 Thanks: 0 Re: Demonstration help Yep, i forgot to change the second one. Sorry, again... [2] Prove that the 1979 first digits after the comma, of the number $(6+\sqrt{35})^{1980}$ , are all digits 9. I can't edit(or even delete) my old posts.
August 26th, 2012, 06:14 AM   #8
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Re: Demonstration help

Quote:
 Originally Posted by Fingolfin I can't edit(or even delete) my old posts.
You can't edit your posts until you have at least 25 posts.

You can't delete you posts if you are not a moderator.

Balarka

.

August 26th, 2012, 06:24 AM   #9
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From: India, West Bengal

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Re: Demonstration help

Quote:
 Originally Posted by Fingolfin Prove that the 1979 first digits after the comma, of the number $(6+\sqrt{35})^{1980}$, are all digits 9.
To be honest, I don't understand what you want to ask.( I observed that $(6+\sqrt{35})^{1980}$ has large numbers of 9's in the later terms of the decimal places of the number).

Balarka

.

 August 26th, 2012, 07:51 AM #10 Newbie   Joined: May 2012 Posts: 6 Thanks: 0 Re: Demonstration help I found the source of the Problem. Sidney Technical highscholl (1996): i) Explain why $(6+\sqrt{35})^{1980} + (6-\sqrt{35})^{1980}$ is a even number. ii) Show that $0 < (6 - \sqrt{35}) < 0.1$ iii) Hence or otherwise prove that the first thousand digits after the decimal point in the value of $(6+\sqrt{35})^{1980}$ are all 9's.

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