For n≥1, let fm=(−1)s where s is the digital sum modulo 2 of the binary representation of m. Prove that 63∑i=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?
No comments:
Post a Comment