I am stuck on this modulo calculation: $$718^{143} \pmod{1260}$$
I have tried using the Euler totient function with no success ($\phi(1260) = 288)$. I think I could solve it using the Chinese remainder theorem but I am guessing there is a faster way.
Any help is appreciated, thanks in advance!
Hints: $718=2\cdot 359$, $\ 1260=2\cdot 630$, $\ \varphi(630)=144$,
So, $359^{143}\equiv 359^{-1}\pmod{630}$ which can be found using the Euclidean algorithm, say it's $x$.
We also need to calculate $2^{142}\pmod{630}$, say it's $y$, and then we can combine them to $$718^{143}=2\cdot 2^{142}\cdot 359^{143}\equiv 2xy\pmod{2\cdot 630}$$ using that $a\equiv b\pmod m\implies 2a\equiv 2b\pmod{2m}$.