Evaluate: (-2407) ÷(-81)
Answers
Link for -20
I don't think the link to -20 is what this article wants. Check to see if it is correct. Georgia guy 00:51, 31 Jan 2005 (UTC)
I just heard an unconfirmed report that a new number has been discovered between 80 and 81. If true, this could have major implications for number 81. —Preceding unsigned comment added by Kackermann (talk • contribs) 14:31, 21 October 2007 (UTC)
Specific and general
That
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81
{\displaystyle {\frac {1}{81}}} exhibits the sequence of digits except 8 is just the base-10 case of the general rule that
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{\displaystyle {\frac {1}{(n-1)^{2}}}} for any base n gives the sequences of digits except n−2. Cf.
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121
{\displaystyle {\frac {1}{121}}} in base 12,
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225
{\displaystyle {\frac {1}{225}}} in base 16 (0.0123456789ABCDF…) to name just two. --109.67.200.119 (talk) 16:13, 10 June 2010 (UTC)
I think you're right. Perhaps we should say that in the article. In fact, I will. — Arthur Rubin (talk) 17:09, 10 June 2010 (UTC)
Thanks. It's of high probability I'm right, because I tested this on a great number of bases using bc, and they all bear it out. However, as with trying out a million triangles of two equal edges and one equal angle and finding out they overlap, that only makes for high probability, not mathematical proof. I don't know a proof. --109.67.200.119 (talk) 17:35, 10 June 2010 (UTC)
Let me see....(I don't know how to do alignments in TeX.)
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{\displaystyle 123\ldots (b-4)(b-3)(b-1)_{b}=1+\sum _{k=0}^{b-2}b^{k}(b-2-k)}
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{\displaystyle =1+\sum _{l=0}^{b-3}\sum _{k=0}^{l}b^{k}}
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{\displaystyle =1+\sum _{l=0}^{b-3}{\frac {b^{l+1}-1}{b-1}}}
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{\displaystyle =1-{\frac {b-2}{b-1}}+{\frac {1}{b-1}}\sum _{l=0}^{b-3}b^{l+1}}
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{\displaystyle ={\frac {1}{b-1}}+{\frac {1}{b-1}}\sum _{l=0}^{b-3}b^{l+1}}
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{\displaystyle ={\frac {1}{b-1}}\sum _{l=0}^{b-2}b^{l}}
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{\displaystyle ={\frac {b^{b-1}-1}{(b-1)^{2}}}.}
(Informative) Also applies to signed-digit bases.
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676
{\displaystyle {\frac {1}{676}}} (676 = square of 26) in balanced base 27 (which stands for three balanced ternary digits much like hexadecimal stands for four binary digits):
0.0123456789
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987654321
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{\displaystyle 0.0123456789ABD{\overline {DCBA987654321}}0123...} (the vinculum marks the negative digits). --79.178.202.78 (talk) 17:06, 26 July 2010 (UTC)
It is also the only number…
Where the sum of its digits equal its square root. Is anyone going to revert this if I make an article change? —Preceding unsigned comment added by Da5id403 (talk • contribs) 23:48, 12 May 2011 (UTC)
Hell's Angels
81 is also the number for the Hells Angels MC. 8=H 1=A — Preceding unsigned comment added by 71.231.251.27 (talk) 16:37, 8 September 2014 (UTC)
Bingo names -
Please see Wikipedia talk:WikiProject Numbers#List of British bingo nicknames for a centralized discusion as to whether Bingo names should be included in thiese articles. Arthur Rubin (alternate) (talk) 23:35, 3 June 2018 (UTC)
1345
179 176.236.222.244 (talk) 21:46, 5 January 2022 (UTC)
Category: WikiProject Numbers articles