easy divisibililty

Number Theory Level 1

7 1 8 m o d 2520 = ? \large 71^8 \bmod 2520=?


The answer is 1.

Muhammad Dihya by Muhammad Dihya , 16, Indonesia

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1 solution

Muhammad Dihya
Mar 18, 2018

7 1 2 = 5041 ≡ 1 ( mod 2520 ) 71^2 = 5041\equiv 1 (\text{mod 2520})

( 7 1 2 ) 3 ≡ 1 3 ( mod 2520 ) (71^2)^3\equiv 1^3 (\text{mod 2520})

7 1 8 ≡ 1 ( mod 2520 ) 71^8\equiv 1 (\text{mod 2520})

so,the answer is 1 \boxed{1}

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