Apéry's theorem

Apéry's theorem - brief summary

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In mathematics, Apéry's theorem is a result in number theory that states the Apéry's constant ζ(3) 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 (n > 0) 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 (n > 1) (though they are conjectured to be irrational).

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