Lets start with a negative number: -7 $$ -7\times3+1=-20\\ -20\div2=-10\\ -10\div2=-5\\ -5\times3+1=-14\\ -14\div2=-7 $$ we can sum up these steps as the following functions: $$ -7\times3+1=-20\\ {-7\times3+1\over2^2}=-5\\ {-7\times3^2+3-2^2\over2^2}=-14\\ {-7\times3^2+3-2^2\over2^3}=-7\\ $$ $$ f...

I found in MO the following equivalent form of the Riemann Hypothesis (RH), that I copy for your convenience: Let $D(N)$ denote the absolute value of the difference between the number of square free integers divisible by an even number of primes and the number of those divisible by an odd number ...