Wednesday, 9 October 2019

number theory - Prove that sum63i=0ficdotleft(n+iright)5=0


For n1, let fm=(1)s where s is the digital sum modulo 2 of the binary representation of m. Prove that 63i=0fi(n+i)5=0.




Since s is the digital sum taken modulo 2 we know that s{0,1}. I don't see a pattern in digital sum of the binary representation modulo 2: 0,1,1,0,1,0,0,1,1,0,0,1,0,1,. How do we prove the sum is equal to zero?

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