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In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ is irrational. That is, the number
cannot be written as a fraction p/q where p and q are integers. The theorem is named after Roger Apéry.
The special values of the Riemann zeta function at even integers 2n can be shown in terms of Bernoulli numbers to be irrational, while it remains open whether the function's values are in general rational or not at the odd integers 2n + 1.
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