This is not for help or anything; just a neat factoid. The number of odd numbers in the nth row of pascal's triangle is , where k is the the number of ones occuring in the binary representation of n.

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- June 24th 2010, 09:53 PMChris11Another really neat theorem!
This is not for help or anything; just a neat factoid. The number of odd numbers in the nth row of pascal's triangle is , where k is the the number of ones occuring in the binary representation of n.

- June 25th 2010, 01:36 AMsimplependulum
The generalization of this theorem is that if the representation of in base prime , then the number of the binomial coefficients which are prime to is .