Find remainder

Find remainder.

21 6 41 / 217 216^{41} / 217


The answer is 216.

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2 solutions

Omkar Kulkarni
Jan 24, 2015

21 6 41 ( 217 1 ) 41 1 216 ( m o d 217 ) 216^{41} \equiv (217-1)^{41} \equiv -1 \equiv \boxed {216} \pmod {217}

even i trid -1 then i tried 216 nice proof

sudoku subbu - 6 years, 4 months ago
William Isoroku
Jan 31, 2015

216 2 1 ( m o d 217 ) { 216 }^{ 2 }\equiv 1\quad (mod\quad 217)

216 41 = ( 216 2 ) 20 216 1 216 ( m o d 217 ) { 216 }^{ 41 }={ ({ 216 }^{ 2 }) }^{ 20 }\cdot 216\equiv 1\cdot 216\quad (mod\quad 217)

Remainder: 216 \boxed{216}

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