[ January 13, 2001 ]
asking for extra material related to a particular theorem...
Honesty compells me to say I couldn't help him further with the project
but found the theorem nevertheless very intriguing as it relates two familar concepts
in a very interesting way namely factorials and binary numbers.
Any natural number N is equal to the sum of the numbers of 1's in its
A few worked out examples to illustrate the topic
Take N = 9
Take N = 79
Just like Kiwoo Song then I am now trying to find information
It was Legendre that first found the results in 1808.
Sum N/q^i from i=0 to inf = [N/q] + [N/q^2] + [N/q^3] + ... + [N/q^n] + 0 + 0 + ...
where [x] = greatest integer less than or equal to x.
He also said that the difference between the number N and the sum
The number of 1s in the binary expression of N is also known as
The proof is not too difficult to find. Can it be found on the web ?
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