Friday, September 2, 2016

Question on modular arithmetic



How does one calculate $3^{(29^{10001})} \mod 35$? I'm just not seeing how to start on it, unless someone could give me a hint? Thanks!


Answer



Hint: To use Euler's theorem, you need to compute $29^{10001} \bmod \phi(35)$, noting that $\phi(35)=24$.



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