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#1 2007-12-17 17:46:26

ganesh
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Registered: 2005-06-28
Posts: 12,919

An interesting number.

Approximately 1.444667861.

The number is the highest value of xth root of x for any value of x.
Further,


is finite when x=1 and infinite when x=2.
The maximum value of x such that

is finite is when x=1.444667861 approximately.
The number is eth root of e, where e or the natural logarithm base is approximately 2.7182818284.


Character is who you are when no one is looking.

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#2 2007-12-21 01:43:25

ganesh
Moderator
Registered: 2005-06-28
Posts: 12,919

Re: An interesting number.

Another interesting number:-

1787109376.

Any power of this number of a number having the last 10 digits as this number will always end in 1787109376, that is, this number.

This is true for 6, 76, 376, 9376, 09376, 109376, 7109376, 87109376, 787109376 also.

I have given a 10 digit number only. It can be calculated to any number of digits and a number n can be produced containing N digits where any power of n or a number having the last digits as n will always have the last N digits as n.


Character is who you are when no one is looking.

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#3 2007-12-21 01:48:21

ganesh
Moderator
Registered: 2005-06-28
Posts: 12,919

Re: An interesting number.

A third interesting number is 1152921504606846976.

This is the smallest number apart from zero and one which is a perfect square, cube, fourth, fifth and sixth power.


The number is also a perfect tenth, twelfth, fifteenth, twentieth, thirtieth and sixtieth power.


Character is who you are when no one is looking.

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