G. Poudyal

When the Divisor Sum Meets the Fibonacci Clock: The Solutions of sigma(n) = pi(n)

Let sigma(n) denote the sum of divisors of n and pi(n) the Pisano period of n (the period of the Fibonacci sequence modulo n). We determine the solutions of sigma(n) = pi(n) below 10^7 and prove the mechanism behind them. The solutions are exactly n = 1, n = 2, the semiprimes pq...

When the Divisor Sum Meets the Fibonacci Clock: The Solutions of sigma(n) = pi(n)

Let sigma(n) denote the sum of divisors of n and pi(n) the Pisano period of n (the period of the Fibonacci sequence modulo n). We determine the solutions of sigma(n) = pi(n) below 10^7 and prove the mechanism behind them. The solutions are exactly n = 1, n = 2, the semiprimes pq...