## Quick Reference

For a positive integer *n*, let *∅*(*n*) be the number of positive integers less than *n* that are relatively prime to *n*. For example, *∅*(12)=4, since four numbers, 1, 5, 7 and 11, are relatively prime to 12. This function *∅*, defined on the set of positive integers, is Euler's function. It can be shown that, if the prime decomposition of *n* is *n*=*p*_{1}^{α}_{1}*p*_{2}^{α}_{2}…*p*_{r}^{αr}, thenEuler proved the following extension of Fermat's Little Theorem: If *n* is a positive integer and *a* is any integer such that (*a*, *n*)=1, then *a*^{ϕ(n)} ≡ 1 (mod *n*).

*Subjects:*
Mathematics.