Apery's Theorem

Apery's theorem is a result in number theory, proved by Roger Apery, stating that Apery's constant, the value of the Riemann zeta function at 3, is irrational, meaning it cannot be written as a ratio of two integers. The theorem stands apart from the situation at even integers, where the zeta function's values were already known to be irrational multiples of powers of pi; whether the zeta function takes irrational values at other odd integers beyond 3 remains an open question, although such irrationality is conjectured. This description is adapted from Wikipedia contributors under CC BY-SA 4.0; changes were made. https://creativecommons.org/licenses/by-sa/4.0/