As a high school student in the mid-1990s, Pace Nielsen encountered a mathematical question that he’s still struggling with to this day. But he doesn’t feel bad: The problem that captivated him, ...

For n a positive integer, let σ(n) denote the sum of the divisors of n. The number n is said to be deficient perfect if σ(n)/n = (2x 1)/x for some x ∊ ℕ. We show that every perfect number has a ...