*Acta Math. Acad. Paed. Nyíregyháziensis*

**15** (1999), 19-26

`www.bgytf.hu/~amapn`

# Some number theoretic applications of the smallest denominator
function

**Zoltán Boros and Árpád Száz**

### Abstract:

We show that the smallest denominator function can be treated with a
minimum amount of number theory. Moreover, this function can be used to
nicely prove a number of fundamental divisibility and irrationality results.

*Mathematics Subject Classification.* 11A99.

*Key words and phrases. *The
smallest denominator function, divisibility and irrationality.