Euler Phi?

Determine: 13 720 m o d 91 { 13 }^{ 720 }\quad \bmod\quad 91 .


The answer is 78.

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1 solution

Otto Bretscher
Dec 1, 2015

1 3 719 ( 1 ) 719 1 6 ( m o d 7 ) 13^{719}\equiv (-1)^{719}\equiv {-1}\equiv 6 \pmod{7} . Now multiply everything with 13 to find 1 3 720 78 ( m o d 91 ) 13^{720}\equiv \boxed{78} \pmod{91} .

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