Can't use Euler's Theorem? I want to use Euler's theorem to calculate the following:
$14^{(2019^{2019})} \mod 60$
$a^{\phi(n)} \equiv 1 \mod n \iff \gcd(a,n) = 1$
Now I start with the outer one first:
$14^{(2019)}\mod 60 \iff \gcd(14,60) = 2$
Now I don't know how can I solve it ...
Can anyone suggest me any hints/further calculations?
Thank you in advance,
Kind Regards.

Here's a way:


*

*Get rid of the gcd,

*then attempt by Euler's theorem, then reformulate mod 60


$$gcd(14,60)=2; gcd(14,15)=1; 14^{2019^{2019}}\equiv 14^{3^3}\equiv -1^3\equiv -1\bmod 15$$  which adding back a factor of 4 coincides with $44 \bmod 60$
