# Lucas congruences for the Apéry numbers modulo *p*^{2}

### (13 pages)

**Abstract.**
The sequence *A*(*n*)_{n >= 0} of Apéry numbers can be interpolated to **C** by an entire function.
We give a formula for the Taylor coefficients of this function, centered at the origin, as a **Z**-linear combination of multiple zeta values.
We then show that for integers *n* whose base-*p* digits belong to a certain set, *A*(*n*) satisfies a Lucas congruence modulo
*p*^{2}.

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